There are 100 employees in a room. 99% are President. How many managers must leave the room to bring down the percentage of President to 98%?
Options:
(A)  1
(B)  2
(C)  46
(D)  50
(E)  97
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We have 99 Presidents and 1 director. That 1 director to compose 2% of the total number of people, there must be 50 people in the room, hence 50 Presidents must leave. So the answer is: (B).
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For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 99 Θ (33 Θ 17)) ?
Options:
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
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(( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 99 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
7 - 3 = 4. So the answer is: (D).
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A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be odd, how many different codes can be created?
Options:
(A) 20
(B) 22
(C) 24
(D) 1
(E) 30
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Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 555 will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 26 = 1. So the answer is: (D).
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