Percents

[BTGmoderatorRO]

Exactly 36% of the numbers in set S are even multiples of 3. If 40% of the even integers in set S are not multiples of 3, what percent of the numbers in set S are not even integers?
(A) 76%
(B) 60%
(C) 50%
(D) 40%
(E) 24%

OA is D

pls can an Expert explain why D is the correct answer? Thanks a lot.

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Hi Roland2rule,

We're told that exactly 36% of the numbers in set S are EVEN multiples of 3 and 40% of the EVEN INTEGERS in set S are NOT multiples of 3. We're asked for the percent of the numbers in set S are NOT EVEN integers. This question involves "sets within sets" and can be solved by TESTing VALUES.

To start, let's TEST 100 total numbers...
36% of the numbers are EVEN multiples of 3 = 36 of the 100 numbers

X = total number of EVEN integers
.4X = EVENS that are NOT multiples of 3
36 = EVENS that ARE multiples of 3

X = .4X + 36
.6X = 36
6X = 360
X = 60

Thus, 60 of the 100 numbers are EVEN INTEGERS. 100 - 60 = 40 numbers that are NOT even integers. 40/100 = 40%

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

Exactly 36% of the numbers in set S are even multiples of 3. If 40% of the even integers in set S are not multiples of 3, what percent of the numbers in set S are not even integers?
(A) 76%
(B) 60%
(C) 50%
(D) 40%
(E) 24%

OA is D

pls can an Expert explain why D is the correct answer? Thanks a lot.

We can let set S have 100 numbers. So 36 even numbers in set S are multiples of 3, and these constitute 60% of the all even integers in set S (since 40% of the even integers in set S are not multiples of 3). Now, if we let E = the total number of even integers in set S, we have:

0.6E = 36

E = 36/0.6 = 360/6 = 60

So we have 60 even integers in S. Since there are 100 numbers in set S, 40 numbers, or 40% of the numbers in set S, are not even integers.

Answer: D