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# M18-35

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Math Expert
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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16 Sep 2014, 00:04
Expert's post
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BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:04) correct 43% (01:10) wrong based on 145 sessions

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If set $$M$$ consists of the root(s) of equation $$2-x^2 = (x-2)^2$$, what is the range of set $$M$$?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135562 [0], given: 12699

Math Expert
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [1], given: 12699

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16 Sep 2014, 00:05
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Official Solution:

If set $$M$$ consists of the root(s) of equation $$2-x^2 = (x-2)^2$$, what is the range of set $$M$$?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

$$2-x^2 = (x-2)^2$$;

$$2-x^2=x^2-4x+4$$;

$$x^2-2x+1=0$$;

$$(x-1)^2=0$$;

$$x=1$$. So, set $$M$$ consists of only one element.

The range of a single element set is 0.

_________________

Kudos [?]: 135562 [1], given: 12699

Intern
Joined: 15 Oct 2013
Posts: 9

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Concentration: Accounting
GPA: 3.01
WE: Accounting (Accounting)

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25 May 2015, 13:43
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.

Kudos [?]: [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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26 May 2015, 05:32
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.

$$2 - x^ 2 = x^2 - 4x + 4$$;

Re-arrange: $$2x^2 - 4x +2 = 0$$;

Reduce by 2: $$x^2 -2x + 1 = 0$$, which is the same as $$(x−1)^2=0$$, so $$x=1$$.
_________________

Kudos [?]: 135562 [0], given: 12699

Intern
Joined: 15 Jan 2014
Posts: 22

Kudos [?]: 17 [0], given: 26

Location: India
Concentration: Technology, Strategy
Schools: Haas '19
GMAT 1: 650 Q49 V30
GPA: 2.5
WE: Information Technology (Consulting)

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10 Feb 2017, 08:47
Hi Bunuel

I think

$$(x−1)^2$$=0 will give 2 equal values for X(1,1) not single value . So range will be 0.

Is this correct ?

Thanks

Kudos [?]: 17 [0], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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10 Feb 2017, 09:00
pranjal123 wrote:
Hi Bunuel

I think

$$(x−1)^2$$=0 will give 2 equal values for X(1,1) not single value . So range will be 0.

Is this correct ?

Thanks

1 and 1 is just one root.
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Kudos [?]: 135562 [0], given: 12699

Intern
Joined: 03 May 2014
Posts: 14

Kudos [?]: [0], given: 3

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16 Nov 2017, 07:56
Bunuel wrote:
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.

$$2 - x^ 2 = x^2 - 4x + 4$$;

Re-arrange: $$2x^2 - 4x +2 = 0$$;

Reduce by 2: $$x^2 -2x + 1 = 0$$, which is the same as $$(x−1)^2=0$$, so $$x=1$$.

How would one know when to reduce the equation as opposed to trying to solve a quadratic equation ax^2 +bx + c when a>1. For example factoring out the 2x^2?

Kudos [?]: [0], given: 3

Re: M18-35   [#permalink] 16 Nov 2017, 07:56
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# M18-35

Moderators: chetan2u, Bunuel

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