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cleetus
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In a survey of political preferences, 78% of those asked Updated on: 05 Feb 2012, 08:43
Originally posted by cleetus on 13 Nov 2010, 14:02.
Last edited by Bunuel on 05 Feb 2012, 08:43, edited 1 time in total.
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C
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Difficulty:

55% (hard)

Question Stats:

68% (02:28) correct 32% (02:37) wrong based on 456 sessions

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In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals.

(A) 10
(B) 12
(C) 17
(D) 22
(E) 30

This is a simple question to answer. Just thought of posting it with solution:

Let p, q and r be the percentages of people who favour exactly two proposals – I & II, II & III and III & I respectively. Then,
50 + (30 - p - 5) + (20 -q - r - 5)
= 78 p+ q + r =12
So, more than one proposal = p + q + r + 5
= 12 + 5 = 17.
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C
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Bunuel
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In a survey of political preferences, 78% of those asked 06 Dec 2010, 08:07
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cleetus
In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals.

(A) 10
(B) 12
(C) 17
(D) 22
(E) 30
Show more

Venn diagram is probably the best way to solve this problem. But you can solve it with formula as well:


\(Total=I+II+III-\{favored \ exactly \ 2}- 2*\{favored \ exactly \ 3}+\{favored \ neither}\)

As {those who favored neither of proposal}=100-78=22 then: \(100=50+30+20-\{favored \ exactly \ 2 \ proposals\}-2*5+22\) --> \(\{favored \ exactly \ 2 \ proposals\}=12\).

Now, those who favored more than one of the 3 proposals equals to \(\{favored \ exactly \ 2 \ proposals\}+\{favored \ exactly \ 3 \ proposals\}=12+5=17\).

Answer: C.

To see how this formula is derived see: formulae-for-3-overlapping-sets-69014.html#p729340

Hope it's clear.
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In a survey of political preferences, 78% of those asked 06 Dec 2010, 07:22
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i quite didnt understand the equation part..

care to elaborate??
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In a survey of political preferences, 78% of those asked 09 Dec 2010, 12:53
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This seems like an awkward question to me. The number favoring more than one proposal should include those who favor all three (since three is greater than one). This would be 80+30+20-78 = 22%. The fact that they provided the information that 5% favor all three proposals suggests to me that the intent of the question was to ask how many favor exactly two of the proposals.

Is this a GMAT question?
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In a survey of political preferences, 78% of those asked 09 Dec 2010, 13:29
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joestrummerlives
This seems like an awkward question to me. The number favoring more than one proposal should include those who favor all three (since three is greater than one). This would be 80+30+20-78 = 22%. The fact that they provided the information that 5% favor all three proposals suggests to me that the intent of the question was to ask how many favor exactly two of the proposals.

Is this a GMAT question?
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Those who favored more than one of the 3 proposals does include those who favored exactly 2 and all 3, but this group doesn't equal to 22%. It equals to \(\{favored \ exactly \ 2 \ proposals\}+\{favored \ exactly \ 3 \ proposals\}=12+5=17\).
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In a survey of political preferences, 78% of those asked 09 Dec 2010, 20:14
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Bunuel, my answer for exactly 2 people was 17 and this was my approach:

100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to

100%=(50+30+20)-(at least 2 people)-5%+22%

when I add 5% to this to get at least more than one of the three proposals I get 22%. Where am I going wrong? why do you multiply by 2*(favored exactly 3 proposals)? Thanks.
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In a survey of political preferences, 78% of those asked 10 Dec 2010, 00:27
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gettinit
Bunuel, my answer for exactly 2 people was 17 and this was my approach:

100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to

100%=(50+30+20)-(at least 2 people)-5%+22%

when I add 5% to this to get at least more than one of the three proposals I get 22%. Where am I going wrong? why do you multiply by 2*(favored exactly 3 proposals)? Thanks.
Show more

Check this: formulae-for-3-overlapping-sets-69014.html#p729340
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In a survey of political preferences, 78% of those asked 10 Dec 2010, 12:10
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Thanks Bunuel very helpful.
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In a survey of political preferences, 78% of those asked 29 Aug 2011, 11:19
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total = I + II + III -2(all three) -(two proposals) + neither
100-neither = 50+30+20 -2(5) -y
78 = 90 - y
y = 12 ............... number of people who voted for two proposals

12+5= 17 .......... people who voted for 2 or 3 proposals
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In a survey of political preferences, 78% of those asked 05 Feb 2012, 08:34
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cleetus
This is a simple question to answer. Just thought of posting it with solution.

In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals:
I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals.
(A) 10 (B) 12 (C) 17 (D) 22 (E) 30
Show more

My solution -
5% of those asked favoured all three of the proposals. The statement does not say that the exactly 5% of the people favoured all three of the proposals. Hence we can apply following formula.

x = I n II + II n III + I n III
5 is I n II n III

78 = 50 + 30 + 20 - x + 5
x = 27. In this value of 27 the intersection between all three sets is counted 3 times so substract it two times i.e., substract 2 *5 = 10

Total folks in favour of two or more proposals = 27 - 10 = 17
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In a survey of political preferences, 78% of those asked 26 Nov 2014, 05:59
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Hi Bunnel,
I get confused where to use the first formula and where to use the second formula . I there any way to identify where to use them ? I usually solve by using the Venn diagrams. So getting confused with the formulas

Thanks, .
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In a survey of political preferences, 78% of those asked 26 Nov 2014, 06:01
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prashd
Hi Bunnel,
I get confused where to use the first formula and where to use the second formula . I there any way to identify where to use them ? I usually solve by using the Venn diagrams. So getting confused with the formulas

Thanks, .
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This is explained here: advanced-overlapping-sets-problems-144260.html
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In a survey of political preferences, 78% of those asked 26 Jan 2021, 21:50
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Total surveyed = (P1 + P2 + P3) - (# who liked exactly 2) - 2(Liked all three)
78 = (50 + 30 + 20) - x - 10
x = 12 <---Total # who like exactly 2

12 + 5 = 17 <----Total who like more than one.

Answer is C.
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In a survey of political preferences, 78% of those asked 30 Oct 2025, 04:23
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