GMAT: Data sufficiency 20

WEBVTT
Kind: captions
Language: en

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We're on problem 87.

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It says an employee is paid 1.5
times the regular hourly

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rate for each hour worked in
excess of 40 hours per week.

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OK.

00:00:15.680 --> 00:00:17.090
So after 40, they get overtime.

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1.5 times.

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Excluding sunday.

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And 2 times the regular
hourly rate for each

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hour worked on sunday.

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So each hour worked on Sunday,
regardless of whether or not

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they're above 40 hours.

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How much was the employee
paid last week?

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OK.

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So let's see.

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Statement one tells us the
employee's regular

00:00:40.730 --> 00:00:43.580
hourly rate is $10.

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$10 per hour is normal.

00:00:46.380 --> 00:00:51.550
Now based on that, we know
what their overtime is.

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Overtime is 1.5 times,
so it's $15 an hour.

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And it tells us that sunday is
double that. $20 an hour.

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All of that was said in the
problem description, I guess

00:01:02.250 --> 00:01:02.970
you could call it.

00:01:02.970 --> 00:01:04.459
But we still don't know how much
they were paid because we

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don't know how many hours they
worked and when those hours

00:01:07.550 --> 00:01:08.210
happened to be.

00:01:08.210 --> 00:01:10.736
So it's still not enough
information.

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Statement number two.

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It says last week the employee
worked a total of 54 hours but

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did not work more than
8 hours on any day.

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OK.

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So let's think about that.

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If you worked no more than 8
hours in a day, how many days

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would you have to work?

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Well you would have to work-- I
guess at minimum, you'd have

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to work 6 days for 8 hours.

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And 1 day you would
work for 6 hours.

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Right?

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Or there's other ways
you could say it.

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You could have all 7 days you
could be working-- for how

00:02:01.380 --> 00:02:03.916
many times does 7 go into--
you could be working 7 6/7

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hours a day.

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Now neither of these help us
because we don't know where

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the hours were allocated.

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We don't know how many of these

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hours ended up on sunday.

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Because that's a critical
question.

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And we know that there
was some overtime

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in some form, right?

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But we don't know if that was
sunday overtime or if that was

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regular overtime.

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Imagine working 7 6/7
hours every day.

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Then you would have 7 6/7
hours for monday through

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friday, then you get some
overtime for saturday as soon

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as you got above 40 hours.

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And then on sunday you would
get paid double.

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But then you have
this situation.

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Maybe sunday is a day
you worked 6 hours.

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Or maybe sunday is one of the
days you worked 8 hours.

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So we don't know.

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So, this problem, there's not
enough information to solve

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this problem.

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88.

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What was the revenue that a
theater received from the sale

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of 400 tickets, some of which
were sold at the full price,

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and the remainder which were
sold at reduced price?

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OK, fair enough.

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The number of tickets sold at
full price-- so this is

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statement number one-- so
immediately we know that there

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were 400 tickets sold.

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And that is the number of
full-priced tickets plus

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reduced priced tickets.

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It's equal to 400, right?

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Wait.

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Some of which were sold at full
price and the remainder

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of which-- oh, they want
to know the revenue.

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OK.

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They want to know the revenue.

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So we have to know how much we
got for each of these tickets

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in order be able to
figure it out.

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So number one.

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The number of tickets sold at
full price were 1/4 of the

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total number of tickets sold.

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So 1/4 times-- what was the
total number of tickets sold?

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Well they already told us that.

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400.

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So it equals 100.

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And then we could just look at
that and that tells us that

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the reduced price were equal
to 300 tickets were sold at

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the reduced price.

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But that still doesn't tell us
the total revenue because we

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don't know how much full
price was or how much

00:04:18.329 --> 00:04:19.630
reduced price was.

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So that's not enough information
just yet.

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Problem two says the full price
of a ticket was $25.

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But we still don't know what
the reduced price is.

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We know the 25 100, or $2,500
were generated from the sale

00:04:37.030 --> 00:04:37.960
of the full-price ticket.

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But the reduced price, they
don't tell us that.

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How much did they reduce
the price, right?

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Some of which were sold at full
price and the remainder

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of which were sold at
a reduced price.

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We don't know what that is.

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It was 25% off?

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50% off?

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We don't know.

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So unless we know the price of
the reduced price ticket, we

00:04:51.820 --> 00:04:52.690
can't figure this out.

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So once again, not enough
information

00:04:54.720 --> 00:04:55.970
to solve the problem.

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Problem 89.

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What is that, a circle?

00:05:06.640 --> 00:05:08.830
The circle represents one
of the operations

00:05:08.830 --> 00:05:11.280
plus, minus and times.

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OK.

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This is interesting.

00:05:12.750 --> 00:05:16.400
So they say a circle represents
one of the

00:05:16.400 --> 00:05:30.150
operations plus minus and times
is k circle l plus m

00:05:30.150 --> 00:05:45.660
equal to k circle l plus
k circle m for all

00:05:45.660 --> 00:05:48.070
numbers k, l, and m?

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Well essentially, what
are they doing?

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They're doing the distributive
property, right?

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They're saying that k-- whatever
this operation times

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l plus n-- is the same thing
as k times whatever this

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operation is with l, plus
k whatever this

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operation is with m.

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And the only places where the
distributive property works is

00:06:05.130 --> 00:06:06.820
either with multiplication
or division.

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And division isn't one
of these properties.

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So essentially this doesn't
work with addition or

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subtraction.

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So if essentially we're able
to prove or disprove that

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multiplication is this operator,
then we have enough

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information.

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This question could be rephrased
as: is circle equal

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to multiplication?

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So if we can answer this with
the statements, then we can

00:06:38.150 --> 00:06:38.980
answer this top one.

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Because only multiplication
works with this.

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Or division, but division isn't
one of the options.

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Statement one says k circle 1 is
not equal to 1 circle k for

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some numbers k.

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Well this immediately tells
me that this is not

00:07:03.090 --> 00:07:04.890
multiplication, right?

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In fact, this tells me that
this is subtraction.

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Right?

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Because the only time where k
minus 1 is different than 1

00:07:11.540 --> 00:07:14.620
minus k, with addition, they'd
always be equal to each other.

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With multiplication they'd
always equal each other.

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So this has to be if you believe
statement one, then

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circle is subtraction.

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Which tells you that this
statement up here is not true.

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So statement one alone is
sufficient to determine

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whether this statement
is true.

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Or another way to phrase
problem, whether circle is

00:07:31.720 --> 00:07:33.230
equal to multiplication.

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So statement one
is sufficient.

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Statement one actually tells
us that the circle is

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subtraction.

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Statement number two.

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Circle represents subtraction.

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OK well they just told
it outright there.

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Well so this and this are
equivalent information and so

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they're enough to determine that
this up here is not true.

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Remember, they're not saying,
is the statement true?

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They're just saying, do you
have enough information to

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figure it out?

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And we know that this isn't
true because circle is

00:08:01.050 --> 00:08:01.770
subtraction.

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And this statement only holds
true if the circle is equal to

00:08:04.860 --> 00:08:06.570
multiplication.

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So each statement alone
is sufficient

00:08:08.750 --> 00:08:10.000
to solve that problem.

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Problem 90.

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How many of the 60 cars sold
last month by a certain dealer

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had neither power windows
nor a stereo?

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OK.

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So it tells us 60 sold.

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And we want to know how
many had neither power

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windows nor a stereo.

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Statement one tells of the 60
cars sold, 20 had a stereo but

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not power windows.

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Fair enough.

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But that still doesn't tell
us how many had neither.

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So let me draw a little circle
Venn Diagram here.

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OK.

00:08:55.050 --> 00:08:57.790
So that's all 60 cars
that were sold.

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That pool right there,
that set.

00:09:00.320 --> 00:09:03.540
20 had stereos with
no power windows.

00:09:03.540 --> 00:09:06.880
So let me draw some Venn
Diagrams. [SNEEZES]

00:09:06.880 --> 00:09:07.980
Excuse me.

00:09:07.980 --> 00:09:09.590
All right.

00:09:09.590 --> 00:09:11.890
That sneeze that I was talking
about a couple of videos ago

00:09:11.890 --> 00:09:14.790
finally happened and
I feel-- [SNEEZES]

00:09:14.790 --> 00:09:15.990
excuse me.

00:09:15.990 --> 00:09:16.410
All right.

00:09:16.410 --> 00:09:17.750
Back to the problem.

00:09:17.750 --> 00:09:19.450
20 had stereos with
no power windows.

00:09:19.450 --> 00:09:25.570
So let's say that this is the
pool that had stereos.

00:09:25.570 --> 00:09:29.690
This is the pool that
had power windows.

00:09:29.690 --> 00:09:32.790
And what we care, actually, is
what had neither stereo nor

00:09:32.790 --> 00:09:33.400
power windows.

00:09:33.400 --> 00:09:36.890
So we care about this outside.

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Oh, that looks tacky.

00:09:37.600 --> 00:09:39.010
That's a little garish.

00:09:39.010 --> 00:09:40.680
But anyway.

00:09:40.680 --> 00:09:44.130
So if this is stereos, this is
power windows, this would be

00:09:44.130 --> 00:09:45.850
stereos and power windows.

00:09:45.850 --> 00:09:48.100
You're saying 20 had stereos
but no power windows.

00:09:48.100 --> 00:09:50.170
So that's this right here.

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So I'll do another fill.

00:09:53.250 --> 00:09:53.500
Yeah.

00:09:53.500 --> 00:09:55.430
That's not pleasant
to look at.

00:09:55.430 --> 00:10:02.840
But this is 20 stereo,
no power window.

00:10:02.840 --> 00:10:06.170
But that alone doesn't tell us
what this green area is.

00:10:06.170 --> 00:10:07.430
So what's the second
statement?

00:10:07.430 --> 00:10:08.770
That's too dark.

00:10:08.770 --> 00:10:14.660
Statement two tells us, of the
60 cars sold, 30 had both

00:10:14.660 --> 00:10:17.265
power windows and a stereo.

00:10:23.080 --> 00:10:25.910
So that tells us that this range
right here-- let me do

00:10:25.910 --> 00:10:30.000
it in another tacky color.

00:10:30.000 --> 00:10:33.040
That tells us that that's
how many had

00:10:33.040 --> 00:10:35.230
power windows and stereos.

00:10:41.650 --> 00:10:43.520
Let me make sure I have
a good color here.

00:10:43.520 --> 00:10:44.580
So that's 30.

00:10:44.580 --> 00:10:46.000
I know that you can't
see that.

00:10:49.290 --> 00:10:50.110
OK.

00:10:50.110 --> 00:10:52.130
So we could answer a couple
of questions.

00:10:52.130 --> 00:10:56.350
We can answer, how many cars
sold had stereos in general?

00:10:56.350 --> 00:10:58.045
Well 50, right?

00:10:58.045 --> 00:11:01.030
20 had a stereo, no
power windows.

00:11:01.030 --> 00:11:03.480
30 had a stereo with
power windows.

00:11:03.480 --> 00:11:05.920
So a total of 50 stereos
were sold.

00:11:05.920 --> 00:11:07.850
We know that.

00:11:07.850 --> 00:11:10.800
50 had stereos.

00:11:10.800 --> 00:11:13.150
But that still doesn't
answer our question.

00:11:13.150 --> 00:11:18.060
Of the 10 that remained-- 60
were total, and there's 10

00:11:18.060 --> 00:11:20.390
left within this space
and this space.

00:11:20.390 --> 00:11:22.070
We don't know how those
10 fall out.

00:11:22.070 --> 00:11:25.410
Maybe 5 had neither and
5 had only power

00:11:25.410 --> 00:11:27.200
windows with no stereo.

00:11:27.200 --> 00:11:32.790
Or maybe there were no cars with
only power windows and no

00:11:32.790 --> 00:11:35.430
stereos, and all
10 had neither.

00:11:35.430 --> 00:11:37.980
So you don't know, even
using both statements.

00:11:37.980 --> 00:11:41.100
So, at least for this one, they
haven't given us enough

00:11:41.100 --> 00:11:44.140
information to figure out
how many had neither.

00:11:44.140 --> 00:11:45.760
They did give us enough
information figure out how

00:11:45.760 --> 00:11:47.510
many stereos got sold,
or how many cars

00:11:47.510 --> 00:11:48.980
with stereos got sold.

00:11:48.980 --> 00:11:49.300
Anyway.

00:11:49.300 --> 00:11:51.150
See you in the next video.


GMAT: Data sufficiency 16

WEBVTT
Kind: captions
Language: en

00:00:00.970 --> 00:00:05.540
We're on problem 73.

00:00:05.540 --> 00:00:08.760
How much did a certain
telephone call cost?

00:00:08.760 --> 00:00:09.050
All right.

00:00:09.050 --> 00:00:10.430
Well, we know nothing so far.

00:00:10.430 --> 00:00:11.400
Statement one.

00:00:11.400 --> 00:00:15.360
The call lasted 53 minutes.

00:00:15.360 --> 00:00:18.060
Well, unless they tell us how
much it costs per minute, that

00:00:18.060 --> 00:00:20.690
still doesn't tell us how
much the call costs.

00:00:20.690 --> 00:00:25.990
Statement two tells us the cost
for the first 3 minutes

00:00:25.990 --> 00:00:31.476
was 5 times the cost for
each additional minute.

00:00:40.610 --> 00:00:42.030
But that still doesn't
help us.

00:00:42.030 --> 00:00:45.370
The cost for the first 3 minutes
might have been $0.05

00:00:45.370 --> 00:00:47.680
a minute, and then we might
have been $0.01 a

00:00:47.680 --> 00:00:49.890
minute after that.

00:00:49.890 --> 00:00:54.343
Or it could have been $0.10 a
minute, and then-- or let me

00:00:54.343 --> 00:00:56.810
make it a multiple of 3-- $0.12
a minute, and then $0.04

00:00:56.810 --> 00:00:59.800
after that.

00:00:59.800 --> 00:01:01.440
Both of these satisfy
that statement.

00:01:01.440 --> 00:01:03.110
And actually, if I have to be
honest, this statement is

00:01:03.110 --> 00:01:04.080
slightly ambiguous.

00:01:04.080 --> 00:01:07.480
Because they're saying the cost
for the first 3 minutes.

00:01:07.480 --> 00:01:09.890
Do they mean that the total cost
for the first 3 minutes

00:01:09.890 --> 00:01:11.830
was 5 times each additional
minute?

00:01:11.830 --> 00:01:15.750
Or was it the cost per minute
of the first 3 minutes was 5

00:01:15.750 --> 00:01:16.800
times additional minutes?

00:01:16.800 --> 00:01:19.450
Well, either way, both
statements combined don't help

00:01:19.450 --> 00:01:21.550
us, because we're not able to
figure out the cost per

00:01:21.550 --> 00:01:24.840
minute, so that we could
apply it to this.

00:01:24.840 --> 00:01:28.500
So they are both useless.

00:01:28.500 --> 00:01:33.460
74.

00:01:33.460 --> 00:01:35.840
In a certain office, 50% of the

00:01:35.840 --> 00:01:37.430
employees are college graduates.

00:01:37.430 --> 00:01:40.440
So let's say 50% college.

00:01:40.440 --> 00:01:41.690
I'll call it C.

00:01:43.990 --> 00:01:47.450
Or I could say 50% of the
employees are college

00:01:47.450 --> 00:01:50.310
graduate, right?

00:01:50.310 --> 00:01:54.120
60% of the employees are
over 40 years old.

00:01:54.120 --> 00:02:01.930
So it says 60% of the employees
equal, we'll call it

00:02:01.930 --> 00:02:05.750
O for over 40.

00:02:05.750 --> 00:02:06.890
I don't know where this
is going, I'm

00:02:06.890 --> 00:02:09.190
just making up numbers.

00:02:09.190 --> 00:02:14.310
And it said if 30% of those over
40 have Master's degrees,

00:02:14.310 --> 00:02:19.500
how many of the employees over
40 have Master's degrees?

00:02:19.500 --> 00:02:20.030
OK.

00:02:20.030 --> 00:02:30.280
So 30% of the over 40 have
Master's degrees.

00:02:30.280 --> 00:02:32.510
I don't know, I'm just trying
to make up some notation.

00:02:32.510 --> 00:02:35.060
How many of the employees over
40 have Master's degrees?

00:02:35.060 --> 00:02:37.280
So we're actually trying to
come up with this number.

00:02:37.280 --> 00:02:40.370
So if we knew how many employees
over 40 there were,

00:02:40.370 --> 00:02:43.270
we would be set, because we'd
just multiply 30% times that.

00:02:43.270 --> 00:02:45.450
If we knew how many employees
there were, we would be all

00:02:45.450 --> 00:02:47.560
set, because we could figure
out the number over 40 and

00:02:47.560 --> 00:02:49.030
then multiply 30 times that.

00:02:49.030 --> 00:02:51.130
So let's see what
they give us.

00:02:51.130 --> 00:02:52.270
Statement one.

00:02:52.270 --> 00:02:55.120
Exactly 100 of the employees
are college graduates.

00:02:58.150 --> 00:03:05.650
So essentially, C is equal
to 100, right?

00:03:05.650 --> 00:03:07.180
And they told us
that 50% of the

00:03:07.180 --> 00:03:08.880
employees are college graduates.

00:03:08.880 --> 00:03:11.240
So that means how many total
employees are there?

00:03:11.240 --> 00:03:15.850
That means that there
are 200 employees.

00:03:15.850 --> 00:03:18.250
100 is 50% of 200.

00:03:18.250 --> 00:03:20.210
So that told us there
are 200 employees.

00:03:20.210 --> 00:03:22.230
If there are 200 employees,
how many

00:03:22.230 --> 00:03:25.790
employees over 40 are there?

00:03:25.790 --> 00:03:27.660
Well, that's O, right?

00:03:27.660 --> 00:03:28.620
O for over 40.

00:03:28.620 --> 00:03:30.830
Well, that's just 60% of 200.

00:03:30.830 --> 00:03:32.300
That's 120.

00:03:32.300 --> 00:03:34.690
And then how many over 40
with Master's degrees?

00:03:34.690 --> 00:03:35.940
Let's that OMD.

00:03:38.940 --> 00:03:40.510
How many of these are there?

00:03:40.510 --> 00:03:42.080
Over 40 with Master's degrees.

00:03:42.080 --> 00:03:46.180
Well, that's 30% of over 40, so
that's 30%-- this is an O--

00:03:46.180 --> 00:03:50.000
this is 30% of this, which is
equal to-- so over 40 with

00:03:50.000 --> 00:03:53.320
Master's degrees
is equal to 36.

00:03:53.320 --> 00:03:54.390
And we would be done.

00:03:54.390 --> 00:03:57.780
So statement one alone
is sufficient.

00:03:57.780 --> 00:04:01.950
I should call it over
40 instead of a 0.

00:04:01.950 --> 00:04:03.030
Don't want to get confused.

00:04:03.030 --> 00:04:04.710
Over 40 with Mater's degrees.

00:04:04.710 --> 00:04:06.210
So statement two.

00:04:06.210 --> 00:04:12.850
Of the employees 40 years
old or less, 25%

00:04:12.850 --> 00:04:15.740
have Master's degrees.

00:04:15.740 --> 00:04:19.279
So that doesn't tell us
anything, really.

00:04:19.279 --> 00:04:22.640
It doesn't tell us how many
employees there are over 40,

00:04:22.640 --> 00:04:24.270
which was one of the things that
we realized we have to

00:04:24.270 --> 00:04:24.650
figure out.

00:04:24.650 --> 00:04:29.060
It doesn't help us figure out
how many total employees there

00:04:29.060 --> 00:04:31.190
are, so we really can't
do this type of logic.

00:04:31.190 --> 00:04:33.795
So it seems fairly useless.

00:04:33.795 --> 00:04:37.330
So yeah, employees 40
years old or less.

00:04:37.330 --> 00:04:38.400
25% of-- no.

00:04:38.400 --> 00:04:40.900
This is a useless piece
of information.

00:04:40.900 --> 00:04:42.630
So the answer is--
what is that?

00:04:42.630 --> 00:04:43.270
I always forget.

00:04:43.270 --> 00:04:43.630
A.

00:04:43.630 --> 00:04:48.180
Statement alone is sufficient
and statement 2 is useless.

00:04:48.180 --> 00:04:53.810
75.

00:04:53.810 --> 00:05:01.010
They ask is rst equal to 1?

00:05:01.010 --> 00:05:08.160
Statement one tells us that
rs is equal to 1.

00:05:08.160 --> 00:05:10.080
This by itself doesn't
help us, right?

00:05:10.080 --> 00:05:13.430
If rs is equal to 1, the only
way that this whole thing is

00:05:13.430 --> 00:05:17.280
going to be equal to 1 is
if t is also equal 1.

00:05:17.280 --> 00:05:20.390
But we don't know that, so-- I
mean, t could be equal to 10.

00:05:20.390 --> 00:05:22.660
So statement one alone
doesn't help us.

00:05:22.660 --> 00:05:29.350
Statement two tells us,
st is equal to 1.

00:05:29.350 --> 00:05:31.710
Well, I can show that even
if we have both of these

00:05:31.710 --> 00:05:33.870
statements, that we still
can't prove this.

00:05:33.870 --> 00:05:37.060
For example, I can come up with
a scenario that meets

00:05:37.060 --> 00:05:39.570
both statements where
this is true.

00:05:39.570 --> 00:05:43.490
Because I can say what if r is
equal to 1, s is equal to 1,

00:05:43.490 --> 00:05:45.680
and t is equal to 1?

00:05:45.680 --> 00:05:49.560
Then we can make both of
these statements true.

00:05:49.560 --> 00:05:53.840
So then, definitely,
rst is equal to 1.

00:05:53.840 --> 00:05:56.870
But let me see if I can
construct something where this

00:05:56.870 --> 00:05:57.720
doesn't hold up.

00:05:57.720 --> 00:06:04.020
So what if r is equal to 6.

00:06:04.020 --> 00:06:10.800
s is equal to 1/6, and
then t is equal to 6.

00:06:10.800 --> 00:06:14.940
So then r times s would still
be equal to 1, right?

00:06:14.940 --> 00:06:16.970
s times t would still
be equal to 1.

00:06:16.970 --> 00:06:18.930
But what is rst now?

00:06:18.930 --> 00:06:22.570
It's 6 times 1/6, times 6,
which is equal to 6.

00:06:22.570 --> 00:06:26.790
So I can satisfy both of these,
but still end up not

00:06:26.790 --> 00:06:29.210
knowing whether it equals 1
or something different.

00:06:29.210 --> 00:06:29.950
I just picked this
arbitrarily.

00:06:29.950 --> 00:06:32.280
You can actually kind of pick
an arbitrary number here and

00:06:32.280 --> 00:06:32.920
set this up.

00:06:32.920 --> 00:06:35.920
So anyway, this is E.

00:06:35.920 --> 00:06:36.730
I think that's E, right?

00:06:36.730 --> 00:06:39.620
Both statements combined
are useless.

00:06:39.620 --> 00:06:39.910
Right.

00:06:39.910 --> 00:06:42.040
They're not sufficient.

00:06:42.040 --> 00:06:43.290
Next problem.

00:06:47.700 --> 00:06:48.465
Turn the page.

00:06:48.465 --> 00:06:50.740
It's problem 76.

00:06:50.740 --> 00:06:52.500
And they've drawn a
nice pie chart for

00:06:52.500 --> 00:06:54.320
us, which I'll reproduce.

00:06:56.970 --> 00:06:58.130
76.

00:06:58.130 --> 00:07:02.150
Total expenses for the 5
divisions of company h.

00:07:02.150 --> 00:07:03.660
Let me draw this pie chart.

00:07:07.950 --> 00:07:08.330
OK.

00:07:08.330 --> 00:07:09.990
And then they have a bunch
of-- let's see, how

00:07:09.990 --> 00:07:10.830
many pies are there?

00:07:10.830 --> 00:07:11.510
There are 5 pies.

00:07:11.510 --> 00:07:14.090
I'll try to draw it the
way they do it.

00:07:14.090 --> 00:07:15.340
So that's one.

00:07:21.350 --> 00:07:22.600
Two.

00:07:25.550 --> 00:07:27.010
Three.

00:07:27.010 --> 00:07:28.302
And they have one more.

00:07:28.302 --> 00:07:28.790
There we go.

00:07:28.790 --> 00:07:31.910
So that looks pretty close
to what they've drawn.

00:07:31.910 --> 00:07:40.300
And then they write, this
is Q, R, S, T, and P.

00:07:40.300 --> 00:07:41.210
O is the center.

00:07:41.210 --> 00:07:44.330
They call this angle, x.

00:07:44.330 --> 00:07:44.750
Fair enough.

00:07:44.750 --> 00:07:47.040
So this is the total expenses
for the 5 divisions.

00:07:47.040 --> 00:07:50.320
So each of these are divisions
for company h.

00:07:50.320 --> 00:07:50.680
76.

00:07:50.680 --> 00:07:54.580
The figure above represents a
circle graph of company h's

00:07:54.580 --> 00:07:57.120
totally expenses broken down
by the expenses for each of

00:07:57.120 --> 00:07:58.780
it's 5 divisions.

00:07:58.780 --> 00:08:02.150
If O is the center of the
circle-- fair enough, so this

00:08:02.150 --> 00:08:03.880
is the center, although I didn't
draw it quite at the

00:08:03.880 --> 00:08:07.690
center-- if O is the center of
the circle, and if company h's

00:08:07.690 --> 00:08:12.120
total expenses are $5.4 million,
what are the expenses

00:08:12.120 --> 00:08:13.160
for division R?

00:08:13.160 --> 00:08:15.080
So the whole thing
is $5.4 million.

00:08:15.080 --> 00:08:19.860
So the whole pie is
$5.4 million.

00:08:19.860 --> 00:08:22.350
And we need to figure out
what R is equal to.

00:08:25.810 --> 00:08:28.380
So the whole expenses
are 360 degrees.

00:08:28.380 --> 00:08:32.350
So whatever fraction x is of 360
degrees, that's going to

00:08:32.350 --> 00:08:34.880
be the fraction that R is
of the total expenses.

00:08:34.880 --> 00:08:36.659
So let's see if they
give us that.

00:08:36.659 --> 00:08:39.520
If we can figure out
what angle x is.

00:08:39.520 --> 00:08:42.520
One, x is equal to 94.

00:08:42.520 --> 00:08:44.049
Well, we're done.

00:08:44.049 --> 00:08:49.810
Because x over the total degrees
in the circle-- so 94

00:08:49.810 --> 00:08:54.420
over 360 degrees-- that's
going to be equal to the

00:08:54.420 --> 00:08:57.800
expenses of division R
divided by the total

00:08:57.800 --> 00:09:01.400
expenses, $5.4 million.

00:09:01.400 --> 00:09:03.390
And this is a trivial
equation to solve.

00:09:03.390 --> 00:09:06.350
So one alone is sufficient.

00:09:06.350 --> 00:09:09.110
Let's see what they give us
for statement number two.

00:09:09.110 --> 00:09:13.150
The total expenses for divisions
S and T are twice as

00:09:13.150 --> 00:09:16.100
much as the expenses
for division R.

00:09:16.100 --> 00:09:23.230
So they're saying that this
right here is twice as much as

00:09:23.230 --> 00:09:24.850
what we're trying
to figure out.

00:09:24.850 --> 00:09:27.740
It's this right here.

00:09:27.740 --> 00:09:30.250
Well, that doesn't help us much,
because P and Q could be

00:09:30.250 --> 00:09:33.330
arbitrarily small or large.

00:09:33.330 --> 00:09:37.380
These two combined could be $2
and this could be $1, right?

00:09:37.380 --> 00:09:39.140
In which case, P and Q
are the bulk of the

00:09:39.140 --> 00:09:40.510
expenses for the company.

00:09:40.510 --> 00:09:43.980
Or maybe these two are
$4 and R is $2,

00:09:43.980 --> 00:09:44.980
which are all possible.

00:09:44.980 --> 00:09:48.200
And these would represent the
rest of the-- whatever.

00:09:48.200 --> 00:09:50.570
It gets you to $5.4 million.

00:09:50.570 --> 00:09:52.580
So statement two is useless.

00:09:52.580 --> 00:09:55.270
So statement one alone is
sufficient and statement two

00:09:55.270 --> 00:09:56.940
does us no good.

00:09:56.940 --> 00:09:58.110
And I'm out of time.

00:09:58.110 --> 00:09:59.920
I'll see you in the
next video.


GMAT: Data sufficiency 18

WEBVTT
Kind: captions
Language: en

00:00:00.910 --> 00:00:05.450
We're on problem 80.

00:00:05.450 --> 00:00:10.760
If a, b, and c are integers,
is a minus b,

00:00:10.760 --> 00:00:11.940
plus c greater-- OK.

00:00:11.940 --> 00:00:22.730
So what they want to know is a
minus b, plus c greater than a

00:00:22.730 --> 00:00:28.470
plus b, minus c?

00:00:28.470 --> 00:00:29.230
Fair enough.

00:00:29.230 --> 00:00:31.520
And if you think about it,
there's an a on both sides of

00:00:31.520 --> 00:00:31.950
this equation.

00:00:31.950 --> 00:00:37.200
So what they're really wanting
to know is minus b plus c

00:00:37.200 --> 00:00:41.660
greater than b minus c?

00:00:41.660 --> 00:00:44.220
Or another way, they're just
trying to say-- I just took a

00:00:44.220 --> 00:00:46.000
from both sides of this
inequality, so it doesn't

00:00:46.000 --> 00:00:47.430
change anything.

00:00:47.430 --> 00:00:50.410
Really what they're asking, if
you just rearrange this, is c

00:00:50.410 --> 00:00:55.480
minus b greater than
b minus c?

00:00:55.480 --> 00:00:57.840
Which is another way of saying,
well, is one of them

00:00:57.840 --> 00:00:58.750
greater than the other one?

00:00:58.750 --> 00:00:59.020
Right?

00:00:59.020 --> 00:01:00.900
If c is greater than b,
this is going to be

00:01:00.900 --> 00:01:01.900
greater than this one.

00:01:01.900 --> 00:01:04.420
If b is greater than c,
this is going to be

00:01:04.420 --> 00:01:05.560
greater than this one.

00:01:05.560 --> 00:01:07.720
So let's look at our
statements now.

00:01:07.720 --> 00:01:09.660
Statement number one.

00:01:09.660 --> 00:01:10.910
b is negative.

00:01:14.120 --> 00:01:17.400
Well, that by itself doesn't
help us much because b could

00:01:17.400 --> 00:01:19.830
be negative, but c could
be even more negative.

00:01:19.830 --> 00:01:22.010
So c could still be smaller
than b, right?

00:01:22.010 --> 00:01:24.650
If b could be minus 5,
c could be minus 6.

00:01:24.650 --> 00:01:26.490
Or c could be plus 6.

00:01:26.490 --> 00:01:30.870
So it really tells us nothing
about c relative to b.

00:01:30.870 --> 00:01:33.595
Statement two says
c is positive.

00:01:36.420 --> 00:01:38.470
So this statement by itself,
once again, it tells us

00:01:38.470 --> 00:01:41.460
nothing about the value
of b relative to c.

00:01:41.460 --> 00:01:43.690
If c is positive, maybe
b is positive as well.

00:01:43.690 --> 00:01:45.190
Maybe b is more positive.

00:01:45.190 --> 00:01:46.530
Or maybe b is negative.

00:01:46.530 --> 00:01:47.340
Who knows?

00:01:47.340 --> 00:01:49.370
But this by itself
doesn't help us.

00:01:49.370 --> 00:01:52.610
But if we use both of these
together, if c is positive and

00:01:52.610 --> 00:01:56.890
b is negative, then we know, if
this is positive, this is

00:01:56.890 --> 00:01:59.740
negative, we know this is
going to be positive.

00:01:59.740 --> 00:02:02.820
And we know that this is
going to be negative.

00:02:02.820 --> 00:02:05.570
Essentially, we know that c is
larger than b, so this will be

00:02:05.570 --> 00:02:06.860
positive and this will
be negative.

00:02:06.860 --> 00:02:07.920
And we can answer
our question.

00:02:07.920 --> 00:02:13.000
If c is larger than
b, this is true.

00:02:13.000 --> 00:02:15.070
The left-hand side is greater
than the right-hand side, or

00:02:15.070 --> 00:02:17.400
this holds good.

00:02:17.400 --> 00:02:19.700
So we need both of the
statements together.

00:02:19.700 --> 00:02:21.290
Both statements together
are sufficient

00:02:21.290 --> 00:02:22.540
to answer this question.

00:02:25.550 --> 00:02:26.950
Switch colors.

00:02:26.950 --> 00:02:29.230
81.

00:02:29.230 --> 00:02:37.470
If a certain animated cartoon
consists of a total of 17,280

00:02:37.470 --> 00:02:42.680
frames on film, how many minutes
will it take to run

00:02:42.680 --> 00:02:43.510
the cartoon?

00:02:43.510 --> 00:02:45.310
So they want to know
how many minutes.

00:02:45.310 --> 00:02:48.240
So essentially, if we knew how
fast the frames have to go

00:02:48.240 --> 00:02:51.140
through-- if it's x frames per
second-- if we knew that

00:02:51.140 --> 00:02:56.130
number, we'd be able to figure
out how long the cartoon runs.

00:02:56.130 --> 00:02:58.520
So statement one is, the
cartoon runs without

00:02:58.520 --> 00:03:01.450
interruption at a rate of
24 frames per second.

00:03:01.450 --> 00:03:03.660
Well, that's exactly what
I just asked for.

00:03:03.660 --> 00:03:06.740
24 frames per second.

00:03:06.740 --> 00:03:08.740
So using just that information,
how many seconds

00:03:08.740 --> 00:03:09.730
does it run?

00:03:09.730 --> 00:03:13.580
Well, it runs 17,280
frames divided by

00:03:13.580 --> 00:03:15.510
24 frames per second.

00:03:15.510 --> 00:03:18.660
This will give you seconds, and
then if you divide this

00:03:18.660 --> 00:03:20.570
number by 60, you'll
get minutes.

00:03:24.670 --> 00:03:27.510
Divide seconds by 60,
you get minutes.

00:03:27.510 --> 00:03:28.200
So this is the answer.

00:03:28.200 --> 00:03:30.830
So one alone was enough to
answer the question.

00:03:30.830 --> 00:03:32.120
What does statement
two give us?

00:03:32.120 --> 00:03:33.850
I'll write it here.

00:03:33.850 --> 00:03:35.080
Statement two.

00:03:35.080 --> 00:03:39.520
It takes 6 times as long to run
the cartoon as it takes to

00:03:39.520 --> 00:03:40.940
rewind the film.

00:03:40.940 --> 00:03:46.030
And it takes a total of
14 minutes to do both.

00:03:46.030 --> 00:03:50.680
6 times as long to run the
cartoon as it takes to rewind.

00:03:58.640 --> 00:04:00.065
Let's say 6 times to play.

00:04:00.065 --> 00:04:01.440
I want different letters.

00:04:04.060 --> 00:04:08.280
So to play the cartoon takes
6 times as long as

00:04:08.280 --> 00:04:12.130
to rewind the cartoon.

00:04:12.130 --> 00:04:14.580
And they say it takes a total
of 14 minutes to do both.

00:04:14.580 --> 00:04:21.600
So they say play plus rewind
is equal to 14.

00:04:21.600 --> 00:04:23.180
And what we want to know
is, how long does it

00:04:23.180 --> 00:04:24.110
take to play the movie?

00:04:24.110 --> 00:04:26.720
And we don't even have to use
that information alone, the

00:04:26.720 --> 00:04:29.670
17,280, but just looking at
this, we have two linear

00:04:29.670 --> 00:04:33.580
equations and two unknowns, so
we can just solved for P.

00:04:33.580 --> 00:04:35.540
P is the playtime
of this movie.

00:04:35.540 --> 00:04:37.860
And if you wanted to figure it
out-- not that you would have

00:04:37.860 --> 00:04:39.050
to, because we would be
done at this point.

00:04:39.050 --> 00:04:41.450
We would say oh, one and two
are each independently

00:04:41.450 --> 00:04:42.890
sufficient to answer
this question.

00:04:42.890 --> 00:04:45.320
But just to show you that
we could figure it out.

00:04:45.320 --> 00:04:48.610
Say R is equal to 14 minus P.

00:04:48.610 --> 00:04:50.200
Then you substitute
that into that.

00:04:53.080 --> 00:04:56.180
You get P is equal
to 6 times R.

00:04:56.180 --> 00:04:59.030
So 6 times 14 is 60, plus 24.

00:04:59.030 --> 00:05:01.440
84 minus 6P.

00:05:01.440 --> 00:05:04.180
You get 7P is equal to 84.

00:05:04.180 --> 00:05:05.880
P is equal to 12 minutes.

00:05:05.880 --> 00:05:06.470
And we'd be done.

00:05:06.470 --> 00:05:07.520
But actually, we didn't have
to do all of that.

00:05:07.520 --> 00:05:09.430
All of that is a
waste of time.

00:05:09.430 --> 00:05:11.080
I just want to prove it to you.

00:05:11.080 --> 00:05:16.780
82.

00:05:16.780 --> 00:05:20.710
A box contains only red chips,
white chips, and blue chips.

00:05:20.710 --> 00:05:23.080
If a chip is randomly selected
from the box, what is the

00:05:23.080 --> 00:05:28.270
probability that the chip will
either be white or blue?

00:05:28.270 --> 00:05:30.000
So essentially, to answer this,
we just have to know

00:05:30.000 --> 00:05:34.160
what proportion of the chips in
the bag are white or blue.

00:05:34.160 --> 00:05:35.090
All right.

00:05:35.090 --> 00:05:38.220
So statement one says, the
probability that the chip will

00:05:38.220 --> 00:05:40.250
be blue is 1/5.

00:05:40.250 --> 00:05:43.880
So probability of blue
is equal to 1/5.

00:05:43.880 --> 00:05:47.080
That also tells us that 1/5 of
the chips in the bag are blue.

00:05:47.080 --> 00:05:50.550
But we don't know what
proportion are white, so we

00:05:50.550 --> 00:05:52.770
still can't answer that
top question.

00:05:52.770 --> 00:05:56.970
Statement two tells us, the
probably that the chip will be

00:05:56.970 --> 00:05:59.300
red is 1/3.

00:05:59.300 --> 00:06:03.270
The probability of red
is equal to 1/3.

00:06:03.270 --> 00:06:06.840
So, once again, just this
alone-- actually, just this

00:06:06.840 --> 00:06:09.010
alone is fine, right?

00:06:09.010 --> 00:06:12.160
I correct myself.

00:06:12.160 --> 00:06:15.080
The probability of getting
white or blue, that's

00:06:15.080 --> 00:06:18.400
probability of white-- we could
write, do set notation,

00:06:18.400 --> 00:06:22.400
white or blue-- that is
just equal to what?

00:06:22.400 --> 00:06:26.490
It's 1 minus the probability
that we get a red.

00:06:26.490 --> 00:06:28.820
Think about that.

00:06:28.820 --> 00:06:30.700
Either this is going to be
true, I'm going to pick a

00:06:30.700 --> 00:06:32.980
white or blue, or I'm
going to pick a red.

00:06:32.980 --> 00:06:36.080
Because there's only red, white,
and blue in the bag.

00:06:36.080 --> 00:06:42.200
So the probability of white or
blue is equal to 1 minus the

00:06:42.200 --> 00:06:47.450
probability of red, which is
equal to 1 minus 1/3, which is

00:06:47.450 --> 00:06:48.530
equal to 2/3.

00:06:48.530 --> 00:06:50.770
So statement two alone
is sufficient.

00:06:50.770 --> 00:06:52.990
And then if we have statement
number two, statement one

00:06:52.990 --> 00:06:56.160
alone is not sufficient.

00:06:56.160 --> 00:06:59.970
83.

00:06:59.970 --> 00:07:02.990
See, this is tricky because, I
think, at least when I first

00:07:02.990 --> 00:07:05.260
read it, I was like, oh, I could
use this and this to

00:07:05.260 --> 00:07:07.230
figure out the probably
of getting a white.

00:07:07.230 --> 00:07:08.100
So I need both statements.

00:07:08.100 --> 00:07:09.750
But we don't even need to know
the probability of a white.

00:07:09.750 --> 00:07:11.940
We just need to know the
probably a white or a blue,

00:07:11.940 --> 00:07:13.710
which is just 1 minus the
probability of red.

00:07:13.710 --> 00:07:16.970
So statement two alone
gets us there.

00:07:16.970 --> 00:07:19.970
Let me do the next problem.

00:07:19.970 --> 00:07:23.030
83.

00:07:23.030 --> 00:07:25.920
If the successive tick marks on
the number line are equally

00:07:25.920 --> 00:07:29.130
spaced, and if x and y are the
numbers designating the

00:07:29.130 --> 00:07:35.150
endpoints of the interval as
shown, what is the value of y?

00:07:35.150 --> 00:07:39.320
OK, so let me see if I can draw
what they have drawn.

00:07:39.320 --> 00:07:40.360
So they have a number line.

00:07:40.360 --> 00:07:42.850
And I probably have to draw the
exact same number of ticks

00:07:42.850 --> 00:07:45.660
as they did.

00:07:45.660 --> 00:07:48.560
So they have 0.

00:07:48.560 --> 00:07:53.290
And then let's see, there's 1
tick, 2 ticks, and then they

00:07:53.290 --> 00:07:55.070
have a third tick.

00:07:55.070 --> 00:07:57.176
And they say this is x.

00:07:57.176 --> 00:07:59.330
And then they have three more.

00:07:59.330 --> 00:08:02.000
1, 2, 3.

00:08:02.000 --> 00:08:04.330
And then they have y.

00:08:04.330 --> 00:08:05.880
And then they have one more.

00:08:05.880 --> 00:08:08.720
And this keeps going
on and on.

00:08:08.720 --> 00:08:14.450
And they ask us, if the ticks
are equally spaced, and if x

00:08:14.450 --> 00:08:16.680
and y are the numbers designated
at the endpoints of

00:08:16.680 --> 00:08:20.640
intervals as shown, what
is the value of y?

00:08:20.640 --> 00:08:22.355
So they're equally spaced, but
they're not telling us that

00:08:22.355 --> 00:08:22.770
these are integers.

00:08:22.770 --> 00:08:25.280
We don't know that this is
1, this is 2, this is 3.

00:08:25.280 --> 00:08:26.380
We don't know that.

00:08:26.380 --> 00:08:35.200
But what we do know is y is
how much further than x?

00:08:35.200 --> 00:08:41.600
So let's see, x is
1, 2, 3 spaces.

00:08:41.600 --> 00:08:47.980
So we could say x is equal to 3
times, let's say, s, where s

00:08:47.980 --> 00:08:51.050
is the length of each interval,
or each tick.

00:08:51.050 --> 00:08:57.550
And y is 1, 2, 3, 4, 5, 6, 7.

00:08:57.550 --> 00:09:01.200
So y is equal to 7s.

00:09:01.200 --> 00:09:02.980
And so we could use this
to come up with a

00:09:02.980 --> 00:09:04.110
relation with x and y.

00:09:04.110 --> 00:09:05.340
This is before they've
done anything.

00:09:05.340 --> 00:09:07.610
This is just looking
at the diagram.

00:09:07.610 --> 00:09:14.050
So we could say that
s is equal to y/7.

00:09:14.050 --> 00:09:18.270
Or if we substitute this back
here, we could say that x is

00:09:18.270 --> 00:09:22.335
equal 3/7 y.

00:09:22.335 --> 00:09:24.710
And actually, you didn't have
to even do this s stuff.

00:09:24.710 --> 00:09:27.890
You could have just said, oh,
well, x is 3/7 as far

00:09:27.890 --> 00:09:28.940
as y is from 0.

00:09:28.940 --> 00:09:30.660
Because these are
equally spaced.

00:09:30.660 --> 00:09:33.290
So just the problem setup, just
looking at it, gives us

00:09:33.290 --> 00:09:35.430
that information.

00:09:35.430 --> 00:09:37.590
But we want to know what the
value of y is, and that by

00:09:37.590 --> 00:09:38.350
itself isn't enough.

00:09:38.350 --> 00:09:40.760
What does statement
one tell us?

00:09:40.760 --> 00:09:42.010
x is equal to 1/2.

00:09:44.260 --> 00:09:45.520
Well, that's enough
to figure out y.

00:09:45.520 --> 00:09:47.730
If x is equal to 1/2, you
just substitute there.

00:09:47.730 --> 00:09:51.310
1/2 is equal to 3/7 y.

00:09:51.310 --> 00:09:53.480
Multiply both sides by 7/3.

00:09:53.480 --> 00:09:55.350
You get y is equal to what?

00:09:55.350 --> 00:09:56.290
7/6.

00:09:56.290 --> 00:09:57.080
And you're done.

00:09:57.080 --> 00:09:57.980
You don't have to solve that.

00:09:57.980 --> 00:09:59.480
You just know that I have
this, I have that.

00:09:59.480 --> 00:10:00.130
I can solve it.

00:10:00.130 --> 00:10:02.870
So one alone is sufficient.

00:10:02.870 --> 00:10:10.500
Statement two tells us, y
minus x is equal to 2/3.

00:10:10.500 --> 00:10:14.390
So once again, we
have two linear

00:10:14.390 --> 00:10:16.510
equations with two unknowns.

00:10:16.510 --> 00:10:18.990
We can just substitute
and solve them.

00:10:18.990 --> 00:10:21.780
And just to prove it to you,
x is equal to 3/7 y.

00:10:21.780 --> 00:10:23.110
I can substitute that
right there.

00:10:23.110 --> 00:10:29.850
So I have y minus 3/7
y is equal to 2/3.

00:10:29.850 --> 00:10:32.430
So 7/7 minus 3/7.

00:10:32.430 --> 00:10:35.460
So that's just to go here.

00:10:35.460 --> 00:10:42.390
7/7 y, so that's 4/7
y is equal to 2/3.

00:10:42.390 --> 00:10:45.075
y is equal to 2/3 times 7/4.

00:10:47.700 --> 00:10:52.870
Which is-- that's 1, this is 2--
which is 7/6 once again.

00:10:56.210 --> 00:10:57.350
See you in the next video.

00:10:57.350 --> 00:11:01.420
So once again, each of these are
independently sufficient

00:11:01.420 --> 00:11:02.945
to answer the question.

00:11:02.945 --> 00:11:04.195
See you soon.


GMAT: Data sufficiency 19

WEBVTT
Kind: captions
Language: en

00:00:00.650 --> 00:00:04.550
We're on problem 84.

00:00:04.550 --> 00:00:09.100
On a company-sponsored cruise,
2/3 of the passengers were

00:00:09.100 --> 00:00:12.010
company employees, and the
remaining passengers were

00:00:12.010 --> 00:00:13.120
their guests.

00:00:13.120 --> 00:00:20.510
So we could say, employees is
equal to 2/3 of passengers.

00:00:20.510 --> 00:00:24.910
And I guess we could also say
that guests are equal to 1/3

00:00:24.910 --> 00:00:26.420
of passengers.

00:00:26.420 --> 00:00:28.020
The remainder are guests.

00:00:28.020 --> 00:00:32.130
If 3/4 of the company employee
passengers were managers, what

00:00:32.130 --> 00:00:36.330
was the number of company
employee passengers who were

00:00:36.330 --> 00:00:38.380
not managers?

00:00:38.380 --> 00:00:38.760
OK.

00:00:38.760 --> 00:00:42.190
So the second statement, in at
least the problem statement,

00:00:42.190 --> 00:00:54.000
it says if 3/4 of the company
employee passengers were

00:00:54.000 --> 00:01:04.540
managers-- so 3/4 of E were
managers, if I read that

00:01:04.540 --> 00:01:11.140
statement-- what was the number
of company employee

00:01:11.140 --> 00:01:14.790
passengers who were
not managers?

00:01:14.790 --> 00:01:22.130
So essentially, they want to
know what 1/4 of E is, right?

00:01:22.130 --> 00:01:23.410
This is what they're asking.

00:01:23.410 --> 00:01:26.940
Because they want to know,
what were the number of

00:01:26.940 --> 00:01:28.920
company employee passengers
that were not managers?

00:01:28.920 --> 00:01:32.260
And 3/4 were managers, 1/4
were not managers.

00:01:32.260 --> 00:01:34.930
So if we could figure out P, we
would be able to figure out

00:01:34.930 --> 00:01:37.640
E, and we'd be able to
figure out 1/4 E.

00:01:37.640 --> 00:01:41.990
If we were able to figure out
guests, we could then use that

00:01:41.990 --> 00:01:44.570
to figure out P, which we could
use to figure out E,

00:01:44.570 --> 00:01:46.020
which we could then
figure out 1/4 E.

00:01:46.020 --> 00:01:48.220
So that's how we should be
thinking about it, not that we

00:01:48.220 --> 00:01:50.150
should be spending that
much time on it.

00:01:50.150 --> 00:01:51.480
Problem number one.

00:01:51.480 --> 00:01:53.720
There were 690 passengers.

00:01:53.720 --> 00:01:55.560
690 is equal to P.

00:01:55.560 --> 00:01:57.660
Well, we'd be done, right?

00:01:57.660 --> 00:02:00.720
Because E is equal to 2/3
P, and then we want to

00:02:00.720 --> 00:02:02.580
know what 1/4 E is.

00:02:02.580 --> 00:02:10.259
So the non-manager employees
would be 1/4 times E, which is

00:02:10.259 --> 00:02:13.580
just 2/3 times P.

00:02:13.580 --> 00:02:14.460
Times 690.

00:02:14.460 --> 00:02:15.480
And that would be our answer.

00:02:15.480 --> 00:02:17.870
So one alone is sufficient.

00:02:17.870 --> 00:02:19.480
And then statement number two.

00:02:19.480 --> 00:02:22.350
There were 230 passengers
who were guests

00:02:22.350 --> 00:02:24.160
of the company employees.

00:02:24.160 --> 00:02:31.040
So they're essentially saying
that guests are equal to 230.

00:02:31.040 --> 00:02:32.850
And then we could use this
information, that guests are

00:02:32.850 --> 00:02:34.570
just 1/3 of P.

00:02:37.830 --> 00:02:39.970
And then, of course, from
there you could solve.

00:02:39.970 --> 00:02:41.890
You could multiply 3 times both
sides of the equation to

00:02:41.890 --> 00:02:46.610
figure out that P
is equal to 690.

00:02:46.610 --> 00:02:48.950
Which is the same information
that they gave in one, which

00:02:48.950 --> 00:02:51.040
was enough to solve
the problem.

00:02:51.040 --> 00:02:53.840
So two alone is also
sufficient.

00:02:53.840 --> 00:02:56.310
So they are each independently
sufficient

00:02:56.310 --> 00:02:59.380
to solve the problem.

00:02:59.380 --> 00:03:02.380
That problem is confusing,
just with the language.

00:03:02.380 --> 00:03:04.700
Company, employee, manager,
passenger,

00:03:04.700 --> 00:03:07.390
guest. It was very confusing.

00:03:07.390 --> 00:03:08.190
85.

00:03:08.190 --> 00:03:12.040
In the x-y plane, does
the point 4 comma

00:03:12.040 --> 00:03:15.460
12 lie on line k?

00:03:15.460 --> 00:03:16.810
OK, this is interesting.

00:03:16.810 --> 00:03:19.560
So let me draw a line k, and
I'll worry about the point 4

00:03:19.560 --> 00:03:21.320
comma 12 later.

00:03:21.320 --> 00:03:22.120
So let's see.

00:03:22.120 --> 00:03:25.650
Let me look at the points that
they do say lie on k.

00:03:25.650 --> 00:03:29.850
So if this is the x-axis,
that's the y-axis.

00:03:29.850 --> 00:03:34.160
Statement one tells us that
the point 1, 7 lies on k.

00:03:34.160 --> 00:03:39.960
So the point 1 comma
7 lies on k.

00:03:43.530 --> 00:03:47.040
And then they also tell us that
the point--- that alone

00:03:47.040 --> 00:03:50.020
isn't going let me know if the
point 4 comma 12 lies on it.

00:03:50.020 --> 00:03:52.652
So 1, 2, 3, 4.

00:03:52.652 --> 00:03:54.280
4 comma 12.

00:03:54.280 --> 00:03:57.400
It might be up here.

00:03:57.400 --> 00:03:59.480
This is the point that
we care about.

00:03:59.480 --> 00:04:00.240
If you can see that.

00:04:00.240 --> 00:04:00.770
Let me scroll down.

00:04:00.770 --> 00:04:03.140
4 comma 12.

00:04:03.140 --> 00:04:05.750
So if the line looks like that,
maybe it goes through,

00:04:05.750 --> 00:04:06.790
but the line could
be like that.

00:04:06.790 --> 00:04:08.830
So statement number one
alone isn't enough.

00:04:08.830 --> 00:04:11.430
Statement number two says the
point minus 2 comma 2.

00:04:19.769 --> 00:04:23.900
x is minus 2, y is positive 2.

00:04:23.900 --> 00:04:25.490
So they're saying
that lies on it.

00:04:25.490 --> 00:04:31.260
Eyeballing this line, k, it
seems like 4 comma 12 could

00:04:31.260 --> 00:04:33.060
very well lie on it.

00:04:33.060 --> 00:04:35.240
But we have to do a little bit
of math to figure it out.

00:04:35.240 --> 00:04:37.120
So first of all, just statement
two by itself

00:04:37.120 --> 00:04:39.530
doesn't help us, because this
line could go anywhere.

00:04:39.530 --> 00:04:43.090
You need two points to just
know what the line is.

00:04:43.090 --> 00:04:45.200
And so how do we figure out
if the point 4 comma

00:04:45.200 --> 00:04:47.630
12 is on this line?

00:04:47.630 --> 00:04:52.390
Well, the easiest way to do it
is to figure out the slope--

00:04:52.390 --> 00:04:53.620
well, I don't know if it's the
easiest way, but it's the way

00:04:53.620 --> 00:04:56.280
I would think about doing it--
is to figure out the slope of

00:04:56.280 --> 00:04:59.100
the line, and then extend that
slope here and see if the

00:04:59.100 --> 00:05:01.440
point 4 comma 12 lies on it.

00:05:01.440 --> 00:05:04.260
So let's see, what's the
slope of this line?

00:05:04.260 --> 00:05:07.870
So when we went up 7 minus 2.

00:05:07.870 --> 00:05:11.270
So the rise is 5.

00:05:11.270 --> 00:05:16.130
When you go up 5, we
went over how much?

00:05:16.130 --> 00:05:17.310
1 minus minus 2.

00:05:17.310 --> 00:05:19.450
We went over 3, right?

00:05:19.450 --> 00:05:22.730
So for every 3 that you move
over, you go up 5.

00:05:22.730 --> 00:05:24.910
That's the easiest way
to think about it.

00:05:24.910 --> 00:05:29.220
So we're going from x is equal
to 1 to x is equal to 4, so

00:05:29.220 --> 00:05:32.700
we're going to the right by 3.

00:05:32.700 --> 00:05:34.810
And so we should
be going up 5.

00:05:34.810 --> 00:05:37.740
So 5 plus 7, sure enough,
is equal to 12.

00:05:37.740 --> 00:05:41.250
So if you just extend the
slope, it does hit the

00:05:41.250 --> 00:05:45.540
point 4 comma 12.

00:05:45.540 --> 00:05:46.660
Well, actually you know what?

00:05:46.660 --> 00:05:50.300
I just wasted a lot of your
time, because we just have to

00:05:50.300 --> 00:05:52.110
know whether the data
is sufficient

00:05:52.110 --> 00:05:53.280
to answer the question.

00:05:53.280 --> 00:05:55.670
We don't have to prove that
the question is true.

00:05:55.670 --> 00:05:58.210
I've just proven to you
that 4 common 12

00:05:58.210 --> 00:05:59.580
does lie on the line.

00:05:59.580 --> 00:06:01.460
But you could have just said,
oh, well, you know what?

00:06:01.460 --> 00:06:05.670
Statement number one gives
me a point on the line.

00:06:05.670 --> 00:06:07.850
That alone isn't enough
to solve the problem.

00:06:07.850 --> 00:06:12.860
Statement number two gives
me another point.

00:06:12.860 --> 00:06:15.750
And then at this point, if
you're really taking the GMAT

00:06:15.750 --> 00:06:17.900
and time matters, you just
say, hey, I got two

00:06:17.900 --> 00:06:19.140
points for this line.

00:06:19.140 --> 00:06:21.150
Two points is everything I need
to know about a line.

00:06:21.150 --> 00:06:23.700
Once I know two points on a
line, I can figure out if any

00:06:23.700 --> 00:06:25.000
other point is on that line.

00:06:25.000 --> 00:06:25.810
I'm done.

00:06:25.810 --> 00:06:28.190
Both statements combined
are sufficient.

00:06:28.190 --> 00:06:30.190
You wouldn't have to do all of
this stuff that I did, which

00:06:30.190 --> 00:06:31.290
would waste your time.

00:06:31.290 --> 00:06:33.010
But just to prove to
you that you could

00:06:33.010 --> 00:06:34.310
figure it, I did that.

00:06:34.310 --> 00:06:34.790
But anyway.

00:06:34.790 --> 00:06:36.750
I have to admit I did waste
your time a little bit.

00:06:36.750 --> 00:06:37.810
You should just immediately
say, oh, I got

00:06:37.810 --> 00:06:38.620
two points on a line.

00:06:38.620 --> 00:06:42.870
Once I have two points, I can
completely figure out if any

00:06:42.870 --> 00:06:45.550
other point lies on that line.

00:06:45.550 --> 00:06:48.220
86.

00:06:48.220 --> 00:06:53.480
The length of the edging that
surrounds circular garden K--

00:06:53.480 --> 00:06:56.720
OK, so we have two gardens,
it looks like.

00:06:56.720 --> 00:07:01.090
So we have circular garden K,
and then we have circular

00:07:01.090 --> 00:07:03.630
garden-- let's see,
what does it say?

00:07:03.630 --> 00:07:06.050
It is 1/2 the length of the
edge that surrounds

00:07:06.050 --> 00:07:08.110
circular garden G.

00:07:08.110 --> 00:07:11.320
So this is circular garden G.

00:07:11.320 --> 00:07:12.400
This is K.

00:07:12.400 --> 00:07:13.810
This is G.

00:07:13.810 --> 00:07:15.770
So they're saying the length of
the edging that surrounds

00:07:15.770 --> 00:07:20.700
circular garden K is 1/2 the
length of the edging that

00:07:20.700 --> 00:07:22.070
surrounds circular garden G.

00:07:22.070 --> 00:07:25.590
So we could say circumference
of K-- right, that's the

00:07:25.590 --> 00:07:29.210
edging that surrounds it--
is equal to 1/2 the

00:07:29.210 --> 00:07:32.230
circumference of G.

00:07:32.230 --> 00:07:33.200
Fair enough.

00:07:33.200 --> 00:07:36.970
What is the area of garden K?

00:07:36.970 --> 00:07:41.420
Assume that the edging
has negligible width.

00:07:41.420 --> 00:07:43.450
Well, a couple of things.

00:07:43.450 --> 00:07:45.860
If we know the circumference,
we know the area, right?

00:07:45.860 --> 00:07:49.640
Because the circumference is 2
pi r, and once we know r, area

00:07:49.640 --> 00:07:50.840
is pi r squared.

00:07:50.840 --> 00:07:54.170
So if we can figure out the
circumference of K, then we

00:07:54.170 --> 00:07:55.520
know its area.

00:07:55.520 --> 00:07:58.210
And likewise, if we know
anything about the radius, or

00:07:58.210 --> 00:08:02.300
the diameter, or the area of
G, we can figure out its

00:08:02.300 --> 00:08:02.750
circumference.

00:08:02.750 --> 00:08:03.600
We know its area.

00:08:03.600 --> 00:08:10.140
We can use the formula, area
equals pi r squared to figure

00:08:10.140 --> 00:08:11.020
out what r is.

00:08:11.020 --> 00:08:12.720
And then once you figure out
what r is, you could just

00:08:12.720 --> 00:08:16.210
figure out that circumference
is equal to 2 pi r.

00:08:16.210 --> 00:08:17.980
So if you have any of this
information, you're able to

00:08:17.980 --> 00:08:19.970
figure out any of
the rest of it.

00:08:19.970 --> 00:08:24.555
So statement number one says,
the area of G is equal to 25

00:08:24.555 --> 00:08:26.580
pi square meters.

00:08:26.580 --> 00:08:27.870
So let me write it.

00:08:31.500 --> 00:08:34.169
So immediately you should say,
hey, if I know the area of G,

00:08:34.169 --> 00:08:36.020
I can figure out the
radius of G.

00:08:36.020 --> 00:08:38.460
And if I know the radius of
G, I can figure out the

00:08:38.460 --> 00:08:39.750
circumference of G.

00:08:39.750 --> 00:08:41.799
If I know the circumference
of G, I can figure out the

00:08:41.799 --> 00:08:43.159
circumference of K.

00:08:43.159 --> 00:08:45.770
If I know the circumference of
K I can figure out the radius

00:08:45.770 --> 00:08:49.780
of K, and if I know the radius
of K, I know the area of K.

00:08:49.780 --> 00:08:51.370
You shouldn't have to calculate
any of that.

00:08:51.370 --> 00:08:52.270
So this is enough.

00:08:52.270 --> 00:08:54.240
This is sufficient.

00:08:54.240 --> 00:08:55.080
Statement two.

00:08:55.080 --> 00:08:57.960
And maybe I'll do that for you,
just to show you that it

00:08:57.960 --> 00:08:58.570
can be done.

00:08:58.570 --> 00:09:00.950
But hopefully it's making
some sense.

00:09:00.950 --> 00:09:04.590
The edging around G is
10 pi meters long.

00:09:04.590 --> 00:09:08.060
So they're actually telling us
that the circumference of G is

00:09:08.060 --> 00:09:09.500
equal to 10 pi.

00:09:09.500 --> 00:09:10.550
So this is even easier.

00:09:10.550 --> 00:09:11.750
They're giving us this.

00:09:11.750 --> 00:09:15.780
That means the circumference of
K is 5 pi, which means that

00:09:15.780 --> 00:09:18.850
we can figure out the radius
of K and we could

00:09:18.850 --> 00:09:19.920
figure out the area.

00:09:19.920 --> 00:09:23.750
So this is also sufficient
to solve the problem.

00:09:23.750 --> 00:09:25.640
And just so you don't take my
word for it, let me just show

00:09:25.640 --> 00:09:27.640
you how quickly you could
figure it out.

00:09:27.640 --> 00:09:33.150
If the area of G is 25 pi, that
means that pi times the

00:09:33.150 --> 00:09:36.960
radius squared of G
is equal to 25 pi.

00:09:36.960 --> 00:09:39.960
That means that the radius
is equal to 5, right?

00:09:39.960 --> 00:09:41.390
Cancel out the pi
on both sides. r

00:09:41.390 --> 00:09:42.590
squared is equal to 5.

00:09:42.590 --> 00:09:43.900
That means the radius is 5.

00:09:43.900 --> 00:09:46.850
That means the circumference
is 2 pi times this.

00:09:46.850 --> 00:09:51.170
So that means that the
circumference of G is equal to

00:09:51.170 --> 00:09:55.060
2 pi times 5, which is 10 pi,
which is exactly what

00:09:55.060 --> 00:09:56.430
statement two told us.

00:09:56.430 --> 00:09:58.100
And then from there, we could
figure out the circumference

00:09:58.100 --> 00:09:59.670
of K, which is 1/2 of that.

00:09:59.670 --> 00:10:03.700
So circumference of K
is equal to 5 pi.

00:10:03.700 --> 00:10:06.500
And then we know that 2 pi
times the radius of K

00:10:06.500 --> 00:10:08.470
is equal to 5 pi.

00:10:08.470 --> 00:10:09.670
Divide both sides by pi.

00:10:09.670 --> 00:10:12.260
We know that the radius
is equal to 5/2.

00:10:12.260 --> 00:10:15.740
And then the area of K would
be pi times this squared.

00:10:15.740 --> 00:10:19.960
So it would be pi times 25/4,
and we'd be done.

00:10:19.960 --> 00:10:21.470
But all of this was
a waste of time.

00:10:21.470 --> 00:10:25.120
I just wanted to show you that
once you have the radius or

00:10:25.120 --> 00:10:27.480
the circumference, or the area
of either of these, you're

00:10:27.480 --> 00:10:29.900
able to figure out
everything else.

00:10:29.900 --> 00:10:31.240
And I'm out of time.

00:10:31.240 --> 00:10:33.050
See you in the next video.


GMAT: Data sufficiency 12

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:05.420
We're on problem 55.

00:00:05.420 --> 00:00:07.790
At a certain picnic each of the
guests was served either a

00:00:07.790 --> 00:00:11.330
single scoop or a double
scoop of ice cream.

00:00:11.330 --> 00:00:12.890
How many of the guests
were served a double

00:00:12.890 --> 00:00:13.720
scoop of ice cream?

00:00:13.720 --> 00:00:16.980
So let's say that d is the
number of guests that were

00:00:16.980 --> 00:00:18.410
served double scoop and
that's what we're

00:00:18.410 --> 00:00:19.830
trying to figure out.

00:00:19.830 --> 00:00:21.760
So what are their statements?

00:00:21.760 --> 00:00:26.120
Statement number one says at the
picnic 60% of the guests

00:00:26.120 --> 00:00:30.000
were served a double
scoop of ice cream.

00:00:30.000 --> 00:00:32.470
So 60% percent of the total were
served a double scoop.

00:00:32.470 --> 00:00:34.810
Let's see if we can write
that algebraically.

00:00:34.810 --> 00:00:41.090
So 60% of the guests.

00:00:41.090 --> 00:00:45.330
So the total number of guests
are the number of guests that

00:00:45.330 --> 00:00:49.110
were served double scoops plus
the number of guests that were

00:00:49.110 --> 00:00:49.760
served single scoops.

00:00:49.760 --> 00:00:52.620
Then we have all of
the guests, right?

00:00:52.620 --> 00:00:54.840
This is this is equal to the
total number of guests.

00:00:58.460 --> 00:01:00.600
And then they tell us that
60% of them were

00:01:00.600 --> 00:01:02.060
served double scoop.

00:01:02.060 --> 00:01:04.069
So the number that were
served double scoop

00:01:04.069 --> 00:01:05.880
is 60% of the total.

00:01:05.880 --> 00:01:08.560
So that statement number one is
just an algebraic equation.

00:01:08.560 --> 00:01:12.290
And this alone though doesn't
help me solve this equation.

00:01:12.290 --> 00:01:14.260
Maybe in the next statement
they'll tell us how many total

00:01:14.260 --> 00:01:15.200
guests there are.

00:01:15.200 --> 00:01:16.270
What this is.

00:01:16.270 --> 00:01:17.820
And that'll help me
but I don't know.

00:01:17.820 --> 00:01:24.520
Let's see, statement number two,
they say a total of 120

00:01:24.520 --> 00:01:26.630
scoops of ice cream were
served to all the

00:01:26.630 --> 00:01:28.560
guess at the picnic.

00:01:28.560 --> 00:01:30.710
So once again, they're telling
us that there are 120 scoops

00:01:30.710 --> 00:01:31.837
of ice cream, they're
not telling us that

00:01:31.837 --> 00:01:33.515
there are 120 guests.

00:01:33.515 --> 00:01:36.460
So let's see, what are the
total number of scoops.

00:01:36.460 --> 00:01:38.970
So there's the number of singles
groups and each of

00:01:38.970 --> 00:01:42.010
those are-- the number of guests
that got singles scoops

00:01:42.010 --> 00:01:44.340
are s and then the number of
scoops is just 1 times that

00:01:44.340 --> 00:01:45.830
because they each
got one scoop.

00:01:45.830 --> 00:01:47.470
And then you have the
number of guests

00:01:47.470 --> 00:01:48.970
that got double scoops.

00:01:48.970 --> 00:01:50.830
But then the number of scoops
they got is going to be 2

00:01:50.830 --> 00:01:52.600
times that.

00:01:52.600 --> 00:01:54.410
So this is the total numbers
scoops, right?

00:01:54.410 --> 00:01:57.040
The number of people that got
single scoops times 1 plus the

00:01:57.040 --> 00:02:00.370
number that got double scoops
times 2 and that is going to

00:02:00.370 --> 00:02:04.040
be equal to the total
number of scoops.

00:02:04.040 --> 00:02:06.470
And this alone isn't going to
help us solve how many double

00:02:06.470 --> 00:02:08.240
scoops were served, it depends
on the singles

00:02:08.240 --> 00:02:09.570
scooped and all of that.

00:02:09.570 --> 00:02:12.800
But if you look at both of these
statements we have two

00:02:12.800 --> 00:02:15.550
linear equations and
two unknowns.

00:02:15.550 --> 00:02:18.080
So at this point you should
immediately say, unless

00:02:18.080 --> 00:02:23.690
somehow these are the same
equation or somehow these are

00:02:23.690 --> 00:02:29.110
two parallel lines, these should
intersect and allow you

00:02:29.110 --> 00:02:30.070
to solve this equation.

00:02:30.070 --> 00:02:32.880
So immediately-- especially if
you don't want to waste time--

00:02:32.880 --> 00:02:35.220
you should say that both
statements together are

00:02:35.220 --> 00:02:36.080
sufficient.

00:02:36.080 --> 00:02:38.080
And if you want me to prove this
to you, let me see if I

00:02:38.080 --> 00:02:39.540
can solve this.

00:02:39.540 --> 00:02:41.520
So I'll do it in a
different color.

00:02:41.520 --> 00:02:44.980
So let me do some
substitution.

00:02:44.980 --> 00:02:50.720
So here we get s is equal
to 120 minus 2d.

00:02:50.720 --> 00:02:52.250
And we can substitute
this back here.

00:02:52.250 --> 00:03:01.250
So you get 0.6 times d plus s,
which is 120 minus 2d, is

00:03:01.250 --> 00:03:03.070
equal to d.

00:03:03.070 --> 00:03:11.340
And so you get 0.6 times 120
minus d is equal to d.

00:03:11.340 --> 00:03:12.580
And what's 0.6 times 120?

00:03:12.580 --> 00:03:14.010
That's 72, right?

00:03:14.010 --> 00:03:18.710
6 times 12 is 72.

00:03:18.710 --> 00:03:24.140
72 minus 0.6d is equal to d.

00:03:24.140 --> 00:03:38.410
So you get 72 is equal to 1.6d
and then 72 divided by 1.6 is

00:03:38.410 --> 00:03:40.220
equal to 45.

00:03:40.220 --> 00:03:43.710
So there, we solved the problem.
d is equal to 45.

00:03:43.710 --> 00:03:45.530
45 double scoops were served.

00:03:45.530 --> 00:03:47.475
And then we could substitute
back into the equation to

00:03:47.475 --> 00:03:49.460
figure how many single scoops or
how many total guests there

00:03:49.460 --> 00:03:50.980
were, but this is all that
we had to figure out.

00:03:50.980 --> 00:03:55.200
And we were able to using both
statements combined.

00:03:55.200 --> 00:03:56.740
To the next problem.

00:03:56.740 --> 00:04:00.100
56.

00:04:00.100 --> 00:04:01.420
What is the value of xy?

00:04:04.810 --> 00:04:05.110
OK.

00:04:05.110 --> 00:04:09.400
Statement number one: they
tell us that y is

00:04:09.400 --> 00:04:10.960
equal to x plus 1.

00:04:13.730 --> 00:04:16.760
And that's not going to tell me
what xy is, I mean there's

00:04:16.760 --> 00:04:19.600
a bunch of x's and a bunch of
different y's depending on

00:04:19.600 --> 00:04:21.680
what I choose.

00:04:21.680 --> 00:04:25.890
Two: they tell us y is equal
to x squared plus 1.

00:04:25.890 --> 00:04:29.860
Once again, this by itself-- it
completely depends on which

00:04:29.860 --> 00:04:31.390
xy's I pick, right?

00:04:31.390 --> 00:04:33.120
I can pick any combination
and get different values.

00:04:33.120 --> 00:04:34.770
You could try that
out yourself.

00:04:34.770 --> 00:04:37.030
But I have two equations
and two unknowns.

00:04:37.030 --> 00:04:39.460
It's a little tricky because one
of them's non-linear, but

00:04:39.460 --> 00:04:41.130
let's see if we can figure
it out with substitution.

00:04:41.130 --> 00:04:43.530
If y equals this and y equals
that, we could set these two

00:04:43.530 --> 00:04:46.040
equal to each other and see
if we can solve for x.

00:04:46.040 --> 00:04:50.520
So we get x plus 1, that's the
first one, should equal this

00:04:50.520 --> 00:04:52.670
one, because they're
both equal to y.

00:04:52.670 --> 00:04:54.720
x squared plus 1.

00:04:54.720 --> 00:04:59.540
Let's see, we can subtract 1
from both sides and you get x

00:04:59.540 --> 00:05:03.080
is equal to x squared.

00:05:03.080 --> 00:05:11.680
And let's see, you could say--
well, you could divide-- if we

00:05:11.680 --> 00:05:17.230
assume that if x does not
equal 0-- so there's two

00:05:17.230 --> 00:05:18.970
solutions here, right?

00:05:18.970 --> 00:05:21.500
x could be equal to 0.

00:05:21.500 --> 00:05:22.480
That's completely legitimate.

00:05:22.480 --> 00:05:24.080
They never told us that
x isn't equal to 0.

00:05:24.080 --> 00:05:25.820
That would satisfy
that equation.

00:05:25.820 --> 00:05:28.140
And then what other
x would satisfy?

00:05:28.140 --> 00:05:33.310
x could be equal to 0 or
x could be equal to 1.

00:05:33.310 --> 00:05:35.570
Either of those are completely
legitimate

00:05:35.570 --> 00:05:38.380
answers here, right?

00:05:38.380 --> 00:05:38.890
Fair enough.

00:05:38.890 --> 00:05:40.680
If x is 0 this is true,
0 equals 0.

00:05:40.680 --> 00:05:43.130
If x is 1, 1 is equal
to 1 squared. x

00:05:43.130 --> 00:05:44.370
can't be negative 1.

00:05:44.370 --> 00:05:45.890
Negative 1 is not equal
to negative 1 squared.

00:05:45.890 --> 00:05:48.625
So these are the two
solutions for x.

00:05:48.625 --> 00:05:50.750
So right now it seems like
it's a little shady, but

00:05:50.750 --> 00:05:53.290
remember, we're not trying to
solve for x or solve for y,

00:05:53.290 --> 00:05:54.330
we're trying to solve for xy.

00:05:54.330 --> 00:05:56.710
So maybe when we solve for y
something, I don't know,

00:05:56.710 --> 00:05:57.920
interesting could happen.

00:05:57.920 --> 00:05:58.970
Let's solve for y.

00:05:58.970 --> 00:06:05.060
If you assume x is equal
to 0 what's y?

00:06:05.060 --> 00:06:09.590
y is equal to 0 plus 1. y is
equal to 1 in this case.

00:06:09.590 --> 00:06:11.790
That's one solution.

00:06:11.790 --> 00:06:13.570
And if you put x is equal
to 0 here you also

00:06:13.570 --> 00:06:14.885
get y is equal 1.

00:06:14.885 --> 00:06:16.770
So this is one set
of solutions.

00:06:16.770 --> 00:06:21.060
And in this reality xy is going
to be equal to what?

00:06:21.060 --> 00:06:24.510
xy is going to be equal
to 0, right?

00:06:24.510 --> 00:06:26.520
0 times 1 is 0.

00:06:26.520 --> 00:06:29.690
Now if x is equal
to 1, what is y?

00:06:29.690 --> 00:06:34.350
Well, if x is equal to 1,
y is equal to 1 plus 1,

00:06:34.350 --> 00:06:36.380
y is equal to 2.

00:06:36.380 --> 00:06:39.330
Well, then xy is equal to 2.

00:06:39.330 --> 00:06:45.700
So using both of the statements,
I still don't know

00:06:45.700 --> 00:06:48.030
whether xy is equal to 0 or 2.

00:06:48.030 --> 00:06:51.290
Someone would have to tell me
that x is not equal to 0, x is

00:06:51.290 --> 00:06:54.350
equal to 0, and only then can I
really solve this equation.

00:06:54.350 --> 00:06:57.080
So the answer to this, even
though we have two equations

00:06:57.080 --> 00:07:00.660
and two unknowns, because one
of them was a quadratic and

00:07:00.660 --> 00:07:04.860
had two solutions, we actually
don't know what xy is.

00:07:04.860 --> 00:07:08.800
So the answer is that the
statements together are not

00:07:08.800 --> 00:07:10.300
sufficient or E.

00:07:10.300 --> 00:07:13.300
That's interesting because they
actually make you do a

00:07:13.300 --> 00:07:16.170
little bit more work than just
eyeballing it and saying, oh,

00:07:16.170 --> 00:07:17.370
I have two equations
to unknowns.

00:07:17.370 --> 00:07:19.720
You've got to be a little
careful when the equations are

00:07:19.720 --> 00:07:22.280
non-linear.

00:07:22.280 --> 00:07:23.660
At least I think that's right.

00:07:23.660 --> 00:07:26.050
Alright, question 57.

00:07:26.050 --> 00:07:32.650
They want to know what
1/x plus 1/y-- some

00:07:32.650 --> 00:07:34.470
police sirens outside.

00:07:34.470 --> 00:07:37.480
I live in Palo Alto, there's
not normally a high crime

00:07:37.480 --> 00:07:38.720
scene here but you never know.

00:07:38.720 --> 00:07:42.060
Anyway, so 1/x plus 1/y.

00:07:42.060 --> 00:07:51.670
So statement number one is
x plus y is equal to 14.

00:07:51.670 --> 00:07:54.480
Actually let me try to simplify
this a little bit.

00:07:54.480 --> 00:07:57.390
If I were to try to add these
two, what could I do?

00:07:57.390 --> 00:08:00.980
Well, when you add two fractions
you have to find a

00:08:00.980 --> 00:08:01.740
common denominator.

00:08:01.740 --> 00:08:05.860
An easy common denominator
for x and y is just xy.

00:08:05.860 --> 00:08:09.050
So 1/x is what over xy?

00:08:09.050 --> 00:08:13.190
Well, it's y/xy plus-- right,
this is the same thing as

00:08:13.190 --> 00:08:17.740
1/x-- plus, and if I had
xy here, what's 1/y?

00:08:17.740 --> 00:08:19.740
Well, that's x/xy.

00:08:19.740 --> 00:08:26.280
So that can be rewritten
as y plus x over xy.

00:08:26.280 --> 00:08:30.070
And now when you rewrite this
statement like this, then

00:08:30.070 --> 00:08:31.380
statement one looks a
little interesting.

00:08:31.380 --> 00:08:33.685
They gave us the numerator at
least. They haven't told us

00:08:33.685 --> 00:08:38.070
what xy is but they told us that
y plus x, or x plus y is

00:08:38.070 --> 00:08:38.860
equal to 14.

00:08:38.860 --> 00:08:42.789
So statement one, it's kind of
part of the puzzle but it's

00:08:42.789 --> 00:08:44.930
not completely helping us.

00:08:44.930 --> 00:08:46.610
Let's see what statement
two tells us.

00:08:46.610 --> 00:08:48.630
I suspect, if this is solveable,
they'll have to

00:08:48.630 --> 00:08:51.200
tell us what xy-- yep, they
tell us what xy is.

00:08:51.200 --> 00:08:54.530
They tell us that xy
is equal to 24.

00:08:54.530 --> 00:08:56.620
So then we're done, right?

00:08:56.620 --> 00:08:58.730
This simplifies to this
and they're telling

00:08:58.730 --> 00:09:00.180
us what this is.

00:09:00.180 --> 00:09:01.120
x plus y is 14.

00:09:01.120 --> 00:09:04.570
So it equals 14/24-- not that
we have to really solve for

00:09:04.570 --> 00:09:06.940
it-- but that is
equal to 7/12.

00:09:06.940 --> 00:09:08.610
But as soon as we got--
you say, oh, that's

00:09:08.610 --> 00:09:09.400
that, that's that.

00:09:09.400 --> 00:09:09.780
You're done.

00:09:09.780 --> 00:09:13.320
You say, both statements
together are sufficient.

00:09:13.320 --> 00:09:16.320
So C.

00:09:16.320 --> 00:09:20.980
58.

00:09:20.980 --> 00:09:27.440
If d denotes a decimal is d
greater than or equal to 0.5?

00:09:31.710 --> 00:09:34.920
They put a 0 here so you make
sure you notice the decimal.

00:09:34.920 --> 00:09:37.200
d, greater than or
equal to 0.5.

00:09:37.200 --> 00:09:42.210
Statement number one tells us
that when d is rounded to the

00:09:42.210 --> 00:09:45.735
nearest 10th the
result is 0.5.

00:09:50.110 --> 00:09:57.650
So let's see, it could be 0.52
and when you round it to the

00:09:57.650 --> 00:10:00.660
nearest 10th it becomes 0.5.

00:10:00.660 --> 00:10:05.410
But on the other hand, it could
be 0.46 and when you're

00:10:05.410 --> 00:10:09.130
round it to the nearest
10th you also get 0.5.

00:10:09.130 --> 00:10:11.650
So since statement one says it
could be either one of these,

00:10:11.650 --> 00:10:13.340
it really doesn't help us to
know whether we're greater

00:10:13.340 --> 00:10:14.230
than or equal to 0.5.

00:10:14.230 --> 00:10:15.660
This one is greater;
this one isn't.

00:10:15.660 --> 00:10:18.360
So statement one by itself
doesn't help.

00:10:18.360 --> 00:10:23.070
Statement two: when d is rounded
to the nearest integer

00:10:23.070 --> 00:10:25.050
the result is 1.

00:10:25.050 --> 00:10:26.860
Now this is interesting.

00:10:26.860 --> 00:10:31.870
If something is rounded to the
nearest integer it has to be

00:10:31.870 --> 00:10:35.420
greater than 0.5, right?

00:10:35.420 --> 00:10:37.590
The smallest number that when
you round it to the nearest

00:10:37.590 --> 00:10:40.830
integer equal to 1
is 0.5, right?

00:10:40.830 --> 00:10:46.850
So it has to be 0.5 or it has to
be 0.51, because 0.499999,

00:10:46.850 --> 00:10:49.350
when you're round it to the
nearest integer, is going to

00:10:49.350 --> 00:10:51.830
be equal 0.

00:10:51.830 --> 00:10:53.750
That's the only way it can
get rounded to 1, if

00:10:53.750 --> 00:10:55.420
you're 0.5 or above.

00:10:55.420 --> 00:11:00.030
So actually statement two alone
is all you need to know

00:11:00.030 --> 00:11:03.700
that d is greater than
or equal to 0.5.

00:11:03.700 --> 00:11:05.990
So that is choice B.

00:11:05.990 --> 00:11:08.065
Statement two alone
is sufficient.

00:11:08.065 --> 00:11:10.170
Alright, I've realized
I've run out of time.

00:11:10.170 --> 00:11:11.930
See you in the next video.


GMAT: Data sufficiency 13

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:03.950
Alright, we're on problem 59.

00:00:03.950 --> 00:00:05.890
59 on page 282.

00:00:05.890 --> 00:00:09.800
If a real estate agent received
a commission of 6% of

00:00:09.800 --> 00:00:12.730
the selling price of a certain
house, what was the selling

00:00:12.730 --> 00:00:14.340
price of the house?

00:00:14.340 --> 00:00:15.600
So the price of the house.

00:00:18.355 --> 00:00:20.880
And they just told us that the
real estate agent received 6%

00:00:20.880 --> 00:00:22.950
percent but that alone
doesn't tell us much.

00:00:22.950 --> 00:00:26.660
So statement number one, they
tell us the selling price

00:00:26.660 --> 00:00:31.360
minus the real estate agent's
commission was $84,600.

00:00:31.360 --> 00:00:33.200
So let's see if we can write
that algebraically.

00:00:33.200 --> 00:00:37.330
The selling price, let's say
p for price, minus the real

00:00:37.330 --> 00:00:39.850
estate agent's commission--
well, the they told us at the

00:00:39.850 --> 00:00:42.240
beginning the real estate
agent received 6% of the

00:00:42.240 --> 00:00:43.410
selling price.

00:00:43.410 --> 00:00:48.040
So that's 0.06, 6%
of the price.

00:00:48.040 --> 00:00:54.480
So they're telling us that
that is equal to $84,600.

00:00:54.480 --> 00:00:55.780
Well, we're done!

00:00:55.780 --> 00:00:59.520
That's a linear equation
with one unknown.

00:00:59.520 --> 00:01:00.650
This is algebra one.

00:01:00.650 --> 00:01:02.070
You can solve for this.

00:01:02.070 --> 00:01:05.540
Let's see, you could say this
is, I mean if you had to,

00:01:05.540 --> 00:01:11.500
0.94p is equal to 84,600 and
then you'd have p is equal to

00:01:11.500 --> 00:01:16.940
84,600 divided by 0.94,
whatever that is.

00:01:16.940 --> 00:01:18.290
But we don't care.

00:01:18.290 --> 00:01:19.730
We just have to know that
we could solve it.

00:01:19.730 --> 00:01:22.820
Well, since we got so close,
let's just solve it.

00:01:22.820 --> 00:01:28.210
84,600 divided by point-- this
is a bad habit when you're

00:01:28.210 --> 00:01:30.400
taking the GMAT, you want to
just know that you could solve

00:01:30.400 --> 00:01:33.070
it-- so the selling price
of the house is $90,000.

00:01:33.070 --> 00:01:33.990
We didn't have to solve that.

00:01:33.990 --> 00:01:36.913
That would be a waste of time
on the real GMAT but I just

00:01:36.913 --> 00:01:40.080
wanted to show you how
easy it was to solve.

00:01:40.080 --> 00:01:43.770
Statement number two,
let's see if this is

00:01:43.770 --> 00:01:45.450
independently useful.

00:01:45.450 --> 00:01:48.200
The selling price was
250% of the original

00:01:48.200 --> 00:01:55.910
purchase price of $36,000.

00:01:55.910 --> 00:01:57.930
We chose p as the selling
price, right?

00:01:57.930 --> 00:01:59.910
The selling price minus-- right,
everything we talked

00:01:59.910 --> 00:02:02.150
about before was the
selling price.

00:02:02.150 --> 00:02:03.410
And now they introduce
this thing called

00:02:03.410 --> 00:02:04.740
the purchase price.

00:02:04.740 --> 00:02:08.860
So the price selling is equal
to-- and that's what we're

00:02:08.860 --> 00:02:11.970
going to figure out--
is equal to 250%.

00:02:11.970 --> 00:02:17.510
So that's 2.5 times the purchase
price of $36,000.

00:02:17.510 --> 00:02:21.470
So times $36,000.

00:02:21.470 --> 00:02:22.420
Actually we didn't have
to write this.

00:02:22.420 --> 00:02:27.700
So the price is 2.5 times 36,000
which is, I'm guessing,

00:02:27.700 --> 00:02:30.180
let's see, 72, yep, it's
$90,000 again.

00:02:30.180 --> 00:02:30.960
We didn't have to do that.

00:02:30.960 --> 00:02:33.820
But once again, this is just a
very-- this is actually not

00:02:33.820 --> 00:02:34.480
even algebra.

00:02:34.480 --> 00:02:36.620
You just have to multiply
2.5 times 36,000 and

00:02:36.620 --> 00:02:37.690
your get the answer.

00:02:37.690 --> 00:02:40.140
So each of these, independently,
are enough to

00:02:40.140 --> 00:02:41.210
solve this problem.

00:02:41.210 --> 00:02:43.340
So that's D.

00:02:43.340 --> 00:02:45.650
Next problem.

00:02:45.650 --> 00:02:46.460
60.

00:02:46.460 --> 00:02:48.360
This yellow's a little
bit over the top.

00:02:48.360 --> 00:02:50.860
Let me do more muted color.

00:02:50.860 --> 00:02:56.950
So they write, if the square
root of x/y is equal to-- what

00:02:56.950 --> 00:02:59.460
does that say-- d?

00:02:59.460 --> 00:03:00.880
Right, is that what
they wrote?

00:03:00.880 --> 00:03:02.810
Is equal to d?

00:03:02.810 --> 00:03:05.160
No, that's equal to n I think.

00:03:05.160 --> 00:03:11.640
Alright, is equal to n, what
is the value of x?

00:03:11.640 --> 00:03:15.770
So statement number one,
they tell us that

00:03:15.770 --> 00:03:20.590
yn is equal to 10.

00:03:20.590 --> 00:03:22.790
Well, this is pretty useful
because this first equation

00:03:22.790 --> 00:03:26.430
they give us, we would just
multiply both sides by y, we

00:03:26.430 --> 00:03:30.620
get square root of x is
equal to yn, right?

00:03:30.620 --> 00:03:32.920
y times both sides
gets us this.

00:03:32.920 --> 00:03:35.760
And if yn is equal to 10 then
we know that the square root

00:03:35.760 --> 00:03:38.240
of x is equal to 10.

00:03:38.240 --> 00:03:41.840
So x is equal to 100.

00:03:41.840 --> 00:03:44.860
So statement one alone
is enough.

00:03:44.860 --> 00:03:47.620
Now what does statement
two do for us?

00:03:47.620 --> 00:03:54.120
They tell us y is equal to
40 and n is equal to 1/4.

00:03:54.120 --> 00:03:57.780
So once again, they substituted
everything else,

00:03:57.780 --> 00:03:59.155
so we just have to
solve for x.

00:03:59.155 --> 00:04:02.250
So both of these individually
are enough so the answer is D.

00:04:02.250 --> 00:04:04.270
But we could solve for
it just for fun.

00:04:04.270 --> 00:04:10.810
We get square root of x/40 is
equal to 1/4 and then you get,

00:04:10.810 --> 00:04:12.632
essentially solving this,
you get square root of

00:04:12.632 --> 00:04:13.600
x is equal to 10.

00:04:13.600 --> 00:04:16.680
And you get the same thing, x
is equal to 100 and you are

00:04:16.680 --> 00:04:18.820
all done, right?

00:04:18.820 --> 00:04:20.450
And you might say, oh, but isn't
there a plus or minus?

00:04:20.450 --> 00:04:23.180
No, because we're saying the
square root of something is

00:04:23.180 --> 00:04:24.070
equal to 10.

00:04:24.070 --> 00:04:25.700
We're not saying the square
root of 100 is what?

00:04:25.700 --> 00:04:27.590
If you said what is the square
root of a 100 you'd say it's

00:04:27.590 --> 00:04:28.395
plus or minus 10.

00:04:28.395 --> 00:04:31.200
But if we said the square root
of something is 10 that

00:04:31.200 --> 00:04:33.150
something has to be 100.

00:04:33.150 --> 00:04:36.490
Anyway, next problem.

00:04:36.490 --> 00:04:39.540
Don't want to dilly-dally.

00:04:39.540 --> 00:04:41.756
61.

00:04:41.756 --> 00:04:45.870
I want to imbue you with a sense
of urgency for the GMAT.

00:04:45.870 --> 00:04:49.150
How many integers are there
between, but not

00:04:49.150 --> 00:04:51.560
including, r and s.

00:04:51.560 --> 00:04:52.850
Fair enough.

00:04:52.850 --> 00:04:55.190
So essentially we have to figure
out what r and s are or

00:04:55.190 --> 00:04:57.000
how far part they are.

00:04:57.000 --> 00:05:05.530
So statement number one-- so
integers between r and s, but

00:05:05.530 --> 00:05:08.090
not including, remember,
not including.

00:05:08.090 --> 00:05:11.180
So statement number one
tells us that r minus

00:05:11.180 --> 00:05:15.990
s is equal to 10.

00:05:15.990 --> 00:05:23.020
Now this is an interesting
question because if we knew

00:05:23.020 --> 00:05:27.300
that r and s were integers then
we could just pick. r

00:05:27.300 --> 00:05:33.110
minus s is, maybe r is equal
to 11 and s is equal to 1.

00:05:33.110 --> 00:05:35.460
And then if you actually just
want me to write it out you

00:05:35.460 --> 00:05:42.420
could say, well, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11.

00:05:42.420 --> 00:05:44.160
How many integers are between
the two and not

00:05:44.160 --> 00:05:45.540
equaling the two?

00:05:45.540 --> 00:05:51.500
1, 2, 3, 4, 5, 6,
7, 8, 9, right?

00:05:51.500 --> 00:05:54.270
But that's if we assume that r
and s are integers and this

00:05:54.270 --> 00:05:57.650
would work for any two sets of
integers that are 10 apart.

00:05:57.650 --> 00:06:01.390
But what happens if we do it
a little bit differently?

00:06:01.390 --> 00:06:06.820
What happens if we say that
this is 1.1, 2.1,

00:06:06.820 --> 00:06:09.260
3.1-- oh no, sorry.

00:06:09.260 --> 00:06:11.820
What if it's between
1.1 and 11.1?

00:06:11.820 --> 00:06:17.000
So if it's 1.1 is r-- oh no,
let me write it this way.

00:06:17.000 --> 00:06:23.140
What if r was 11.1 and
s was equal to 1.1?

00:06:23.140 --> 00:06:26.030
Then what are the integers
between them but not equal?

00:06:26.030 --> 00:06:31.550
So if you start at 1.1 you would
have 2, 3, 4, 5, 6, 7,

00:06:31.550 --> 00:06:36.750
8, 9, 10-- and now 11 would be
included because 11 would

00:06:36.750 --> 00:06:39.320
still be less than r-- 10, 11.

00:06:39.320 --> 00:06:44.750
So now you have 1, 2, 3,
4, 5, 6, 7, 8, 9, 10.

00:06:44.750 --> 00:06:47.410
So statement number one is
actually not enough because

00:06:47.410 --> 00:06:48.870
they didn't tell us that
r and s are integers.

00:06:48.870 --> 00:06:51.580
If r and s were integers
then the answer would

00:06:51.580 --> 00:06:53.440
be 9 in this case.

00:06:53.440 --> 00:06:55.620
But if r and s are not
integers then the

00:06:55.620 --> 00:06:57.020
answer could be 10.

00:06:57.020 --> 00:07:00.590
So statement number one alone
is not enough, the answer

00:07:00.590 --> 00:07:02.960
could be 9 or 10.

00:07:02.960 --> 00:07:05.130
OK, what does statement
number two do for us.

00:07:05.130 --> 00:07:06.400
Let me do it in a
different color.

00:07:06.400 --> 00:07:08.802
Statement number two.

00:07:08.802 --> 00:07:10.530
This is an interesting
problem.

00:07:10.530 --> 00:07:17.280
There are 9 integers between,
but not including, r plus 1

00:07:17.280 --> 00:07:20.460
and s plus 1.

00:07:20.460 --> 00:07:20.790
OK.

00:07:20.790 --> 00:07:21.780
So this is interesting.

00:07:21.780 --> 00:07:24.460
So they're telling us that there
are 9 integers between r

00:07:24.460 --> 00:07:25.920
plus 1 and s plus 1.

00:07:25.920 --> 00:07:27.830
So, I mean, actually just
looking at it, inspection, you

00:07:27.830 --> 00:07:29.450
could say, oh, well then
there are 9 integers

00:07:29.450 --> 00:07:31.320
between r and s.

00:07:31.320 --> 00:07:32.380
And they say but
not including.

00:07:32.380 --> 00:07:33.230
So this is enough.

00:07:33.230 --> 00:07:35.850
This alone is sufficient and
you don't need statement

00:07:35.850 --> 00:07:36.310
number one.

00:07:36.310 --> 00:07:38.710
Statement number one actually
doesn't get you anywhere.

00:07:38.710 --> 00:07:41.510
So let me prove to you that if
there are 9 integers between r

00:07:41.510 --> 00:07:45.945
plus 1 and s plus 1-- Well,
think of it this way: if there

00:07:45.945 --> 00:07:51.370
are 9 integers between r plus 1
an s plus 1, if you subtract

00:07:51.370 --> 00:07:55.690
1-- so s is one of the one's
that are between-- now I want

00:07:55.690 --> 00:08:04.480
to make sure I do this right--
Let me think of a good way for

00:08:04.480 --> 00:08:05.790
me to prove it to you.

00:08:05.790 --> 00:08:07.270
Well, I'll just do it
with an example.

00:08:07.270 --> 00:08:15.440
So let's say that the example
is 11 and 1, right?

00:08:15.440 --> 00:08:17.110
This isn't a proof but I just
want to give you the

00:08:17.110 --> 00:08:18.370
intuition, right?

00:08:18.370 --> 00:08:22.500
So if r is 11 and s is 1, so
then you would have 12-- well,

00:08:22.500 --> 00:08:23.560
I don't want to do
it that way.

00:08:23.560 --> 00:08:26.390
The easiest way to think about
it is, it doesn't matter how

00:08:26.390 --> 00:08:31.420
much you are adding-- if you
add the same amount to both

00:08:31.420 --> 00:08:35.700
the bottom of the range and the
top of the range it should

00:08:35.700 --> 00:08:37.990
not change the total
number of integers

00:08:37.990 --> 00:08:40.020
that are between them.

00:08:40.020 --> 00:08:43.429
So there would also be 9
integers between r minus

00:08:43.429 --> 00:08:46.010
1 and s minus 1.

00:08:46.010 --> 00:08:48.800
You're just shifting the range
along the number line but

00:08:48.800 --> 00:08:51.350
you're not going to actually
change the number of integers

00:08:51.350 --> 00:08:52.160
in between them.

00:08:52.160 --> 00:08:56.280
So if they're 9 integers between
r plus 1 and s plus 1,

00:08:56.280 --> 00:08:59.570
there's going to be 9 integers
between r and s.

00:08:59.570 --> 00:09:01.170
So two is all you need.

00:09:01.170 --> 00:09:03.090
Hopefully that's a satisfactory
explanation.

00:09:03.090 --> 00:09:05.050
I didn't want to go into
something rigorous when we're

00:09:05.050 --> 00:09:08.460
trying to imbue you with
a sense of urgency.

00:09:08.460 --> 00:09:10.090
See if I have time for
the next problem.

00:09:13.600 --> 00:09:19.030
OK, 62.

00:09:19.030 --> 00:09:23.330
What is the number of members of
club x who are at least 35

00:09:23.330 --> 00:09:26.060
years of age.

00:09:26.060 --> 00:09:29.970
So number who's age is at least
35, so it's greater than

00:09:29.970 --> 00:09:30.920
or equal to 35.

00:09:30.920 --> 00:09:33.590
The number who's age is true.

00:09:33.590 --> 00:09:33.740
OK.

00:09:33.740 --> 00:09:37.700
They tell us statement number
one, exactly 3/4 of the

00:09:37.700 --> 00:09:42.880
members of club x are under
35 years of age.

00:09:42.880 --> 00:09:50.130
So 3/4 are less than 35.

00:09:50.130 --> 00:09:55.490
That is fair enough but that
doesn't tell us the number

00:09:55.490 --> 00:09:57.410
that are at least 35.

00:09:57.410 --> 00:09:59.290
This tells us the percentage.

00:09:59.290 --> 00:10:06.840
This tells us that 1/4 above or
we say 1/4 greater than or

00:10:06.840 --> 00:10:08.880
equal to 35.

00:10:08.880 --> 00:10:15.610
1/4 of total members greater
than or equal to 35.

00:10:15.610 --> 00:10:17.250
So it tells us proportion
but it doesn't tell

00:10:17.250 --> 00:10:18.300
us the total amount.

00:10:18.300 --> 00:10:22.240
And I just got the 1/4 from 3/4
are less than 35, 1/4 are

00:10:22.240 --> 00:10:25.350
going to be greater than or
equal to 35 years of age.

00:10:25.350 --> 00:10:27.030
So one by itself doesn't
help us.

00:10:27.030 --> 00:10:29.610
Let's see what two
does for us.

00:10:29.610 --> 00:10:32.670
The 64 women-- am I reading
the same problem?

00:10:32.670 --> 00:10:36.370
OK, yeah-- the 64 women in club
x constitute 40% of the

00:10:36.370 --> 00:10:37.740
club's membership.

00:10:37.740 --> 00:10:38.690
OK.

00:10:38.690 --> 00:10:43.725
So 64 is equal to 40% of
the total membership.

00:10:46.520 --> 00:10:47.980
Now we're set, right?

00:10:47.980 --> 00:10:50.490
Because we can use this equation
to figure out the

00:10:50.490 --> 00:10:51.860
total membership.

00:10:51.860 --> 00:10:53.380
Call it t for total.

00:10:53.380 --> 00:10:57.310
t is going to be equal
to 64 divided by 0.4.

00:10:57.310 --> 00:10:59.840
They just told us that
essentially 64 is 40% percent

00:10:59.840 --> 00:11:00.190
of the total.

00:11:00.190 --> 00:11:01.740
They said it's the women
and all that.

00:11:01.740 --> 00:11:04.960
But they could've just told us
that 64 is 40% of the total.

00:11:04.960 --> 00:11:06.830
So then you can solve
for the total.

00:11:06.830 --> 00:11:09.220
And then you substitute that
here and you say 1/4 of the

00:11:09.220 --> 00:11:13.050
total are 35 five years or older
and you get what we were

00:11:13.050 --> 00:11:14.440
trying to solve for.

00:11:14.440 --> 00:11:22.800
And so the answer is 1/4 times
64/0.4, and whatever that is,

00:11:22.800 --> 00:11:23.900
you can put it in
your calculator.

00:11:23.900 --> 00:11:26.500
But all we had to care is that
when you use both of these

00:11:26.500 --> 00:11:30.500
equations combined, you're able
to solve for the number

00:11:30.500 --> 00:11:33.180
that are greater than or
equal to 35 years old.

00:11:33.180 --> 00:11:35.530
And each statement alone isn't
sufficient, so you need both

00:11:35.530 --> 00:11:36.240
statements.

00:11:36.240 --> 00:11:39.470
And that is C, both statements
together are sufficient.

00:11:39.470 --> 00:11:41.310
See you in the next video.