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

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

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.

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48% of respondents to a survey consisted of those who used both M and [#permalink]
x+y = 48
x = 48-y

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

44-26.5 = 17.5
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Re: 48% of respondents to a survey consisted of those who used both M and [#permalink]
Bunuel
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

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
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48% of respondents to a survey consisted of those who used both M and [#permalink]
Imagine a Venn Diagram [( A (B) C ) D].
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 [Both M+N and Neither M/N] ..........St1
Statement 2 => C+D = 44 [Not M] ........................................St2
Statement 3 => B+C = 39 [N] ..............................................St3

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

Therefore, 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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Bunuel
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

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