Survey results indicated that 76 percent of the people in a city

Question

Survey results indicated that 76 percent of the people in a city approved of the mayor’s actions. However, because of issues with the way the survey had been conducted, 25 percent of the respondents who actually did not approve had been counted as if they did approve. What percentage of the respondents actually approved?

(A) 51%
(B) 57%
(C) 68%
(D) 70%
(E) 84%

Source: Marty Murray Coaching

Show Answer

Official Answer

C

(A) 51%
(B) 57%
(C) 68%
(D) 70%
(E) 84%

Source:  Marty Murray Coaching

MartyMurray · Accepted Answer

Survey results indicated that 76 percent of the people in a city approved of the mayor’s actions. However, because of issues with the way the survey had been conducted, 25 percent of the respondents who actually did not approve had been counted as if they did approve. What percentage of the respondents actually approved?

(A) 51%
(B) 57%
(C) 68%
(D) 70%
(E) 84%

Source: Marty Murray Coaching

Show Answer

Official Answer

C

This question exemplifies a common characteristic of GMAT PS questions: while the math involved is relatively simple, the reading aspect of answering the question is tricky. Specifically, it's easy to confuse the percentages involved and end up calculating a value other than the one asked for.

Percentage who actually approved: A

Percentage who actually did not approve: 100 - A

A + 0.25(100 - A) = 76

0.75A + 25 = 76

0.75A = 51

A = 68

(A) 51%

(B) 57%

(C) 68%

(D) 70%

(E) 84%

Correct answer:   C

findingmyself · Answer

Approved 
 Not Approved 
 Total 
 
  Current 
 76 
 24 (0.75 of Actual Not Approved) 
 100 
 
  Actual 
  Since Actual not approved is 32
Aporived will be 100-32=68  
  0.75* Actual NA=24
Actual NA=24(4/3)=32  
 100 
 
  % Actual 
 68% 
 32% 
 100%

MegB07 · Answer

Hi, could someone tell whats wrong with this approach?

Assuming 100 to be total number of people surveyed. Out of which 76 approved. 25% of 76 who didnt approve but were counted as approved = 19. So 76 - 19 = 57 is total number of people who approved.

I understand the reasoning given for the correct answer. Dont understand where i am going wrong here.

MartyMurray · Answer

The key to getting this question correct is understanding what the 25 percent mentioned is a percentage of.

Is the 25 percent really a percentage of those who were counted as approving by the survey?

Take another look at what the passage says the 25 percent is a percentage of.

lily123400 · Answer

I solved for this in a quick way:
We have 100 people with 76 approvals comprised of real approve + fake approve.
We know 76+ Not approve = 100.
to set up the equation we have:
1/4(Don't approve) + Real Approve = 76
Don't approve = 100-76 (Not approve) + 1/4(24+x)

So the equation is
1/4(24+x) + (76-x) = 76
solve and you get x = 8
76-8 = 68

AnishTrivedi99 · Answer

Can be solved directly from options. Look at C, If 68% actually approved, that means 32% didn't. It says 1/4th of those who didn't approve were counted as Approved. So 8% extra, hence the equations matches, 68 + 8 = 76% as approved. (Considered the total to be 100)

vallequalle · Answer

I would say this question is a good example for using the method of trying out the options since you can calculate the results pretty fast.

You can start with Option B or C since you can determine if you need to go "up or down" to get to the correct answer with just 2 calculations maximum.

Option C looks very tempting since it is divisible by 4 so we start with that one:

100 % - 68 % = 32 %
32 % / 4 = 8%
68 % + 8 % = 76 %

Lucky hit but even if it was not the correct answer you could get to it by just repeating those three easy steps with Option B or D. If we would land under 76 % we would know that we have to increase the input (value in the option) and vice versa. So imo this is a good way to save some time on a 705-805 marked question.

Hope this helps anyone as much as it helped me getting the correct answer in under 1 minute!

kevincan1 · Answer

wonderful question!

Survey results indicated that 76 percent of the people in a city

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	Approved	Not Approved	Total
Current	76	24 (0.75 of Actual Not Approved)	100
Actual	Since Actual not approved is 32 Aporived will be 100-32=68	0.75* Actual NA=24 Actual NA=24(4/3)=32	100
% Actual	68%	32%	100%

GMAT Problem Solving (PS) Questions

Survey results indicated that 76 percent of the people in a city

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards