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]

05 Feb 2012, 18:20

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36% (02:10) wrong

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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]

05 Feb 2012, 19:03

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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, 23:03, edited 1 time in total.

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

05 Feb 2012, 19:09

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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.

Answer: D.
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ps [#permalink]

06 Jun 2012, 17:36

some people are successful, because they have been fortunate enough and some people earn success, because they have been determined.....

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Re: ps [#permalink]

06 Jun 2012, 18:00

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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Re: ps [#permalink]

06 Jun 2012, 18:02

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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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Re: ps [#permalink]

06 Jun 2012, 22:13

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I think its a lot easier to see with a table:

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Re: ps [#permalink]

07 Jun 2012, 11:13

alchemist009 wrote:

Merging similar topics. Please ask if anything remains unclear.
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

04 Mar 2013, 00:36

rxs0005 wrote:

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

Answer: D

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

04 Mar 2013, 00:36

rxs0005 wrote:

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

Answer: D

Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] 04 Mar 2013, 00:36

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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.

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