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48% of respondents to a survey consisted of those who used both M and

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48% of respondents to a survey consisted of those who used both M and  [#permalink]

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New post 01 Nov 2019, 05:45
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E

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Question Stats:

63% (03:27) correct 37% (03:16) wrong based on 65 sessions

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48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?

(A) 21.5%
(B) 20%
(C) 19.5%
(D) 18.5%
(E) 17.5%


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Re: 48% of respondents to a survey consisted of those who used both M and  [#permalink]

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New post 01 Nov 2019, 06:41
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Bunuel wrote:
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?

(A) 21.5%
(B) 20%
(C) 19.5%
(D) 18.5%
(E) 17.5%

Are You Up For the Challenge: 700 Level Questions



We can use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of respondents , and the two characteristics are:
- Used M or didn't use M
- Used N or didn't use N

With the given information, we can set up our matrix as follows:
Image
IMPORTANT: I let x = number of respondents who used BOTH M and N, and I let y = the number who used NEITHER M nor N",
So, from the first sentence, we can write: x + y = 48
ASIDE: I placed a star in the box that the question asks us to find.


Next, since the two boxes on the right column must add to 44, the top-right box must be 44-y
Image

Next, since the two boxes on the top row must add to 39, the top-right box must be 39-x
Image

Since we have two ways to represent the top-right box, we can write: 44-y = 39-x
Add x to both sides to get: 44 - y + x = 39
Subtract 44 from both sides to get: -y + x = -5
Rearrange to get: x - y = -5

We now know that:
x + y = 48
x - y = -5

Add the equations to get: 2x = 43
Solve: x = 21.5

If x = 21.5, then the top-right box = 39 - 21.5 = 17.5

Answer: E

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:
[you-tube]https://www.youtube.com/watch?v=jK-tiBrrf04[/you-tube
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Re: 48% of respondents to a survey consisted of those who used both M and  [#permalink]

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New post 01 Nov 2019, 06:43
1
Bunuel wrote:
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?

(A) 21.5%
(B) 20%
(C) 19.5%
(D) 18.5%
(E) 17.5%


Are You Up For the Challenge: 700 Level Questions


From below table structure,
Image

Y + 48 - X = 44
--> Y = X - 4 ....... (1)

X + Y = 39
--> Y = 39 - X ........ (2)

From (1) & (2),
X - 4 = 39 - X
--> 2X = 43
--> X = 21.5%
--> Y = 39 - 21.5 = 17.5%

Only N = Y = 17.5%

IMO Option E
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Re: 48% of respondents to a survey consisted of those who used both M and  [#permalink]

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New post 01 Nov 2019, 08:05
-----UM--NUM---total
UN---x--39-x---39
NUN--56-x--y--61
total---56--44--100
44-y+x=39
x-y=-5
and given ; x+y=48
solve ; 2x=43
x= 21.5
so NUM UN = 39-21.5 ; 17.5%
IMO E



Bunuel wrote:
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?

(A) 21.5%
(B) 20%
(C) 19.5%
(D) 18.5%
(E) 17.5%


Are You Up For the Challenge: 700 Level Questions
GMAT Club Bot
Re: 48% of respondents to a survey consisted of those who used both M and   [#permalink] 01 Nov 2019, 08:05
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