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# If 60 percent of respondents answered Yes to the first quest

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Manager
Joined: 20 Nov 2009
Posts: 114
If 60 percent of respondents answered Yes to the first quest  [#permalink]

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Updated on: 11 Aug 2010, 07:52
1
4
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:39) correct 13% (01:56) wrong based on 104 sessions

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If 60 percent of respondents answered Yes to the first question of a survey, 35 percent answered Yes to the second question, and 15 percent answered No to both questions, what percent of the respondents answered Yes to both questions?

A. 10%
B. 25%
C. 40%
D. 55%
E. 70%

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Originally posted by aiming4mba on 11 Aug 2010, 07:10.
Last edited by aiming4mba on 11 Aug 2010, 07:52, edited 1 time in total.
Intern
Joined: 02 Aug 2010
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Re: problem solving  [#permalink]

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11 Aug 2010, 07:24
1
There are no answers to choose from.

10% said Yes to both Questions
Intern
Joined: 04 Jul 2010
Posts: 16
Re: problem solving  [#permalink]

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11 Aug 2010, 14:15
1
i dont get it...how did you get A?
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Re: problem solving  [#permalink]

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11 Aug 2010, 18:50
I did not get any of the options listed but here is my approach.

60 % answered Yes to first question -- let us take 12 out of 20.

35 % answered No to the second question -- take 7 out of 20.

Total -- 19 out of 40 -- 47.5 % (which is not in the options.)

I am clueless as to how the answer is 10%. Someone kindly enlighten me.....
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Joined: 14 May 2010
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Re: problem solving  [#permalink]

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11 Aug 2010, 19:40
If you make a table you'll get the answer in 30 seconds.

Just make it like this:

Q1-yes | Q1-no
Q2-yes
Q2-no
Total=100

it's a 2x2 table.
Manager
Joined: 20 Mar 2010
Posts: 66
Re: problem solving  [#permalink]

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11 Aug 2010, 23:05
1
We can also use Venn diagram to solve this question.

If F is set of respondents who answered Yes to First and S is the set of respondents who answered Yes to 2nd question , we need to find F^S (respondents who answered Yes to both)

Total = F+S -F^S+Neither
100 = 60+35 -F^S+15
F^S =10%
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Re: problem solving  [#permalink]

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11 Aug 2010, 23:14
2nd Y 2nd N Total
1st Y 10 50 60

1st N 25 15 40

Total 35 65 100

Hence 10% -> A. Hope I am right!
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Joined: 11 Aug 2010
Posts: 1
Re: problem solving  [#permalink]

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11 Aug 2010, 23:24
60% - yes to 1st Q
35% - yes to 2nd Q
15% - no to both
?% - yes to both (lets us say ? is x)

60-x+x+35-x+15=100
x=10% which is Answer A
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Joined: 24 Aug 2009
Posts: 3
Re: problem solving  [#permalink]

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12 Aug 2010, 13:32
Assuming that there is no maybe answer

------------
| YY| YN | -> 60%
------------
| NY| 15 | -> 40% (100%-60%)
------------
35% 65% (100%-35%)

From here:
YN + 15 = 65 -> YN = 50
YY + YN = 60 -> YY = 10

Check:
NY + 15 = 40 -> NY = 25
YY + NY = 35 -> YY = 10
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Re: problem solving  [#permalink]

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12 Aug 2010, 14:36
crack700 wrote:
We can also use Venn diagram to solve this question.

If F is set of respondents who answered Yes to First and S is the set of respondents who answered Yes to 2nd question , we need to find F^S (respondents who answered Yes to both)

Total = F+S -F^S+Neither
100 = 60+35 -F^S+15
F^S =10%

Got it thanks
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Re: If 60 percent of respondents answered Yes to the first quest  [#permalink]

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17 Oct 2013, 17:35
Assuming 100 people responded to the survey...

60% said yes to q1 or 60 people
35% said yes to q2 or 35 people

So as of right now the pool of people who said yes is at 95...

But we know 15% said no to both (or 15 people)
Which means 85% said at least one yes (85 people)
so if there are 95 'YES' responses but only 85 people who could have said yes, that means 10 of them said yes to both.
10/100 = 10%
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Re: If 60 percent of respondents answered Yes to the first quest  [#permalink]

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05 Jan 2019, 16:00
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Re: If 60 percent of respondents answered Yes to the first quest   [#permalink] 05 Jan 2019, 16:00
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