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

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Director
Joined: 07 Jun 2004
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Location: PA
Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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05 Feb 2012, 18:20
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10
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65% (hard)

Question Stats:

61% (01:45) correct 39% (01:48) wrong based on 277 sessions

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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%

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Joined: 28 Dec 2011
Posts: 4668
Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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Updated on: 05 Feb 2012, 23:03
2
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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Originally posted by mikemcgarry on 05 Feb 2012, 19:03.
Last edited by mikemcgarry on 05 Feb 2012, 23:03, edited 1 time in total.
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Joined: 02 Sep 2009
Posts: 46319
Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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05 Feb 2012, 19:09
1
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, 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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06 Jun 2012, 18:02
1
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, 22:13
1
I think its a lot easier to see with a table:

Senior Manager
Joined: 13 Aug 2012
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Concentration: Marketing, Finance
GPA: 3.23
Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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04 Mar 2013, 00:36
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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Senior Manager
Joined: 13 Aug 2012
Posts: 443
Concentration: Marketing, Finance
GPA: 3.23
Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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04 Mar 2013, 00:36
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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Intern
Joined: 02 May 2013
Posts: 24
WE: Engineering (Aerospace and Defense)
Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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25 Jul 2013, 23:14
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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Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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21 Apr 2016, 13:45
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
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink]

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14 Aug 2017, 11:55
Let the number of numbers in set be 600 (An easy looking multiple of 36 and 40)
As per question we can use venn diagram to solve this question easily. For the same download the PDF and check.
Attachments

Exactly 36%.pdf [64.64 KiB]

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Re: Exactly 36% of the numbers in set S are even multiples of 3.   [#permalink] 14 Aug 2017, 11:55
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