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

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rxs0005
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Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  05 Feb 2012, 18:20
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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%
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mikemcgarry
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  Updated on: 05 Feb 2012, 23:03
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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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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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Bunuel
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  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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Re: ps [#permalink] New post  06 Jun 2012, 18:00
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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] New post  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] New post  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: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  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

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

Answer: D
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  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] New post  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] New post  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.
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Exactly 36% of the numbers in set S are even multiples of 3 [#permalink] New post  27 Jun 2018, 23:40
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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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  28 Jun 2018, 02:07
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mystiquethinker 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%


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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  03 Apr 2020, 08:21
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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%


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
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Re: Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  02 Jan 2023, 02:33
We are told that 36% of the numbers in the set are even multiples of 3, and that 40% of the even numbers in the set are not multiples of 3.

Assume that there are 100 numbers in the set .
36 even multiples of 3, which account for 60% of all the even numbers in the set
By setting up simple equation:
36=6/10(E)
E=60, where E represents the total amount of even numbers in the set.
100-60=40, 40/100 is the percentage of total even numbers in the set, which is choice D and which is the correct answer.
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Exactly 36% of the numbers in set S are even multiples of 3. [#permalink] New post  02 Jan 2023, 22:32
We can use a double matrix to plot the information as shown below.

Let the total number in the set = 100

Number of even integers = x

Number of non even integers = 100 - x

Given: 40% of the even integers in set S are not multiples of 3

Therefore 60% of the even integers in set S are multiples of 3

\(\frac{60}{100} * x = 36\)

\(x = 60\)

Question: What percent of the numbers in set S are not even integers

\(\frac{100 - x }{ 100 }\)

\(\frac{40 }{ 100} = 40\)%

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