Exactly 36% of the numbers in set S are even multiples of 3. : GMAT Problem Solving (PS)
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# Exactly 36% of the numbers in set S are even multiples of 3.

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Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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05 Feb 2012, 17:20
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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

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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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05 Feb 2012, 18:03
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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 05 Feb 2012, 22:03, edited 1 time in total.
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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05 Feb 2012, 18:09
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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.

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06 Jun 2012, 17:00
36% of numbers in set S = 60% of even numbers in set S
=> 100% of even numbers in set S = (36/60)*100 = 60% of numbers in set S
=> Percentage of numbers in set S that are not even = 100% - 60% = 40%

Choice D
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06 Jun 2012, 17:02
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So there's three kinds of numbers:
Even Multiples of 3 = x
Even Non-Multiples of 3 = y
Non-Even Numbers = z
Together they make up all the numbers, so x + y + z = 1

We are solving for z.

What we know:
36% of the numbers in set S are even multiples of 3, so x = .36.
40% of the even integers in set S are not multiples of 3, so (Even Non Multiples of 3) = 40% of all Even Numbers, in other words:
y = 40%*(y+x), so y = .24

So solving for z, we have:
100 = .36 + .24 + z
z = .40 = 40%
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06 Jun 2012, 21:13
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I think its a lot easier to see with a table:

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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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03 Mar 2013, 23:36
rxs0005 wrote:
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%

Use Double Matrix

----------even---/-----odd------
---3---- / 36
---not3-/ .4X
Total---/ X / ?

.6X = 36
X = 60

If 60 are even the 40 percent are not even

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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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03 Mar 2013, 23:36
rxs0005 wrote:
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%

Use Double Matrix

----------even---/-----odd------
---3---- / 36
---not3-/ .4X
Total---/ X / ?

.6X = 36
X = 60

If 60 are even the 40 percent are not even

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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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25 Jul 2013, 22:14
Given 40% even numbers are not multiples of 3 and 36%of total set is even multiples of 3
i.e, 60% even numbers are multiple of 3
Let x be even numbers among set of 100
0.6*x=36
x=60
Not x =40
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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21 Apr 2016, 10:31
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Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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21 Apr 2016, 12:45
let S=all numbers in set S
E=all even integers in set S
.36S=1-.40E=.60E
E/S=3/5=.60S=60% of numbers in set S that are even integers
1-.60S=.40S=40% of numbers in set S that are not even integers
Exactly 36% of the numbers in set S are even multiples of 3.   [#permalink] 21 Apr 2016, 12:45
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