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  Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]
New postPosted: Sun Feb 05, 2012 6:20 pm 
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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%
[Reveal] Spoiler: OA
D

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mikemcgarry
  Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]
New postPosted: Sun Feb 05, 2012 7:03 pm 
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Hi, there. I'm happy to help with this. :)

Let S be the total number of elements in set S.

We know that 0.36*S is the number of even multiples of three.

Let N be the number of even numbers.

We know 0.40*N are even numbers not multiple of three. This also means, 0.60*N are even numbers that are multiples of three.

Therefore:

0.06*N = 0.36*S

N = (0.36/0.60)*S = (36/60)*S = (6/10)*S = 0.60*S = 60% of S

So even numbers are 60% of S. That means, 40% of S are not even integers. Answer = D (Bunuel, thanks for catching that.)

Does that make sense? Please let me know if you have any questions on this.

Mike :)

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Last edited by mikemcgarry on Sun Feb 05, 2012 11:03 pm, edited 1 time in total.

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Bunuel
  Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]
New postPosted: Sun Feb 05, 2012 7:09 pm 
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mikemcgarry wrote:
Hi, there. I'm happy to help with this. :)

Let S be the total number of elements in set S.

We know that 0.36*S is the number of even multiples of three.

Let N be the number of even numbers.

We know 0.40*N are even numbers not multiple of three. This also means, 0.60*N are even numbers that are multiples of three.

Therefore:

0.06*N = 0.36*S

N = (0.36/0.60)*S = (36/60)*S = (4/10)*S = 0.40*S = 40% of S

So even numbers are 40% of S. That means, 60% of S are not even integers. Answer = B

Does that make sense? Please let me know if you have any questions on this.

Mike :)


Everything is correct except the red part with a typo: it should be N=0.6S --> even numbers are 60% of S --> 40% of S are not even integers.

Answer: D.

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