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

Question

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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BrentGMATPrepNow · Accepted Answer

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:
 https://i.imgur.com/bygAjOX.png 
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 
 https://i.imgur.com/Ee1fXcl.png

Next, since the two boxes on the top row must add to 39, the top-right box must be  39-x 
 https://i.imgur.com/FvFJ3ib.png

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:
 https://www.youtube.com/watch?v=jK-tiBrrf04[/you-tube

CareerGeek · Answer

From below table structure, 
 https://gmatclub.com/forum/download/file.php?mode=view&id=51365

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

Archit3110 · Answer

-----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

metalhead2593 · Answer

Name
m = people who used only M
n = people who used only N
B = people who used both M and N
NULL = people who used none of them

m + n + B + NULL = 100%
B + NULL = 48%

44% of respondents did not use M, so n+NULL = 44%
39% used N, so n+B=39%

So, (n+NULL) + (n+B) = 2n + (N+B) = 2n + 48% = 44% + 39% = 83%. n = 17.5%
If the question asks for m (number of people who used only M), simply take 100%-48%-17.5% for the value of m.

effatara · Answer

Let the total number of respondents be 200, the number who used only M be 'm', the number who used only N be 'n', the number who used both be 'mn' and the number who used neither be 'nn'. Then:

The number of those who used both plus the number who used neither=mn+nn=48% of 200=96.......(i)
The nbr of those who did not use M= Nbr who used only N + Nbr used neither=n+nn=44% of 200=88....(ii)
The nbr of those who used N= Nbr who used only N plus the nbr used both=n+mn=78..........................(iii)
Subtracting eqn.(iii) from (ii), we get nn-mn=10....(iv)
Subtracting (iv) from (i), we get mn=43
Substituting the value of 'mn' in (iii), we get n=35 which is 17.5% of 200. ANS: E

ScottTargetTestPrep · Answer

Letting b = both and n = neither, we have b + n = 48. Furthermore,  not M = N only + neither , and  N only = N - both , so we have:

not M = N - both + neither

44 = 39 - b + n

b - n = -5

Adding together b + n = 48 and b - n = -5, we have:

2b = 43

b = 21.5

Since N only = N - both, we have N only = 39 - 21.5 = 17.5.

Answer: E

fireagablast · Answer

x+y = 48
x = 48-y

x+44-y = 39
48-y+44-y = 39
y = 26.5

44-26.5 = 17.5

Kinshook · Answer

Given: 
1. 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 
2. 44% of respondents did not use M. 
3. 39% used N.

Asked: What percent of respondents used only N?

*************** M *************** ~M ***************Total
N*************. x% ************** x% - 4% **********2x%-4% = 39%; x% = 43%/2 = 21.5%
~N**********. ****************48% -x%
Total******** **************** 44%

The percent of respondents used only N = x% - 4% = 21.5% - 4% = 17.5%

IMO E

Cinderace · Answer

Imagine a Venn Diagram  .
A = Only M
B = Both M and N
C = Only N
D = Neither M nor N

Assume that there are 100 Participants

Statement 1 => B+D = 48   ..........St1
Statement 2 => C+D = 44   ........................................St2
Statement 3 => B+C = 39   ..............................................St3

We have to find the Value of C
(St1 - St2) + St3 =>  +(B+C)= 48-44+39 = 43 => 2B = 43 => B=21.5
Substituting B in St3 => C = 39-B = 17.5

Therefore, E

desertEagle · Answer

b+d = 48 (1)
c+d = 44 (2)
b+c = 39 (3)

(1) + (2) - (3)
2d=92-39 = 53
d=26.5

Putting value of d in (2)
c=21.5

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

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