In a survey, voters were asked whether they approve or disapprove of

Question

https://gmatclub.com/forum/download/file.php?id=88485 In a survey, voters were asked whether they approve or disapprove of a certain pair of policies, and their answers are shown in the table above. If a total of 1,000 voters answered survey questions about both policies, how many voters said that they approve of policy A but did not say that they approve of policy B? (1) 275 voters said that they approve of policy B but did not say that they approve of policy A. (2) 325 voters said that they approve of neither policy A nor policy B. GMAT-Club-Forum-k53nmkzf.png

Bunuel · Accepted Answer

GMATNinja Video Solution: https://www.youtube.com/watch?v=TRlVgm7RdmE GMAT-Club-Forum-2bv4uvb1.png

Sonatomar · Answer

Could anyone give me the solution.

minimaodio · Answer

B Approve 
 B Disapprove 
 B Neutral

A Approve 
 a 
 b 
 c 
 400 
 
  A Disapprove 
 d 
 e 
 f 
 400 
 
  A Neutral 
 g 
 h 
 i 
 200

500 
 200 
 300 
 1000

percyboi66 · Answer

Is it not possible that a person disapproving of B could remain neutral on A? I don't think statement 2 is sufficient. Answer = A in my opinion

akshatpatodia · Answer

I would make a 2x2 grid here

X axis for A - (i) Approve A (ii) Disprove or Neutral 
Y axis for B - (i) Approve B (ii) Disprove or Neutral

Either statement helps us complete the gride and answer the question

egmat · Answer

Hi percyboi66,

I see exactly where the worry is coming from, but it's actually answering a sub-question we don't need to answer.

Look closely at what the question asks:  "approve of policy A but did  not  approve of policy B."  The phrase "did not approve of B" already bundles together  both  the disapprove-B people  and  the neutral-on-B people. So we never have to separate them - whether a non-approver of B is disapproving or neutral makes no difference to the count.

Also, the case you raise - someone who disapproves of B and is neutral on A - isn't even part of our target group, because they don't approve of A. So it can't make our answer wobble.

Now watch Statement (2) pin everything down with no ambiguity:

- Approve neither A nor B =  325 , so approve  at least one  =  1000  -  325  =  675 .
- From the table, approve A =  400  and approve B =  500  (both fixed).
- By the overlap rule:  675  =  400  +  500  - (approve both), so approve both =  900  -  675  =  225 .
- Approve A but not B =  400  -  225  =  175 .

That's a single, fixed value - so Statement  (2)  is  sufficient  on its own.

Notice it lands on the  same 175  that Statement  (1)  gives, which is why each statement alone works and the answer is  D .

The takeaway: before judging sufficiency, make sure you're tracking the exact group the question defines. "Did not approve B" is one combined bucket - splitting it into disapprove vs. neutral was extra work the question never asked for.

Answer: D

egmat · Answer

Hi Sonatomar,

Happy to walk through the whole thing. The key is to read what each row gives you and figure out the one missing piece: how many voters approve of  both  policies.

Setup.  From the table:
- Approve A =  400 
- Approve B =  500 
- Total voters =  1,000

The question asks for  approve A but not B . That's just:

approve A but not B = (approve A) - (approve  both ) =  400  - (both)

So the entire question reduces to one unknown:  how many approve both?  Whatever pins that number down is  sufficient .

Statement (1)

275  approve B but not A. By the same logic:

approve B but not A = (approve B) - (both) =  500  - (both) =  275

So  both = 225 . Then approve A but not B =  400  -  225  =  175 . One definite value -  sufficient .

Statement (2)

325  approve  neither . So the number who approve  at least one  policy =  1,000  -  325  =  675 .

Using the overlap rule:

at least one = A + B - both =  400  +  500  - both =  900  - both =  675

So again  both = 225 , and approve A but not B =  400  -  225  =  175 . One definite value -  sufficient .

Putting it together

Each statement on its own nails down the "approve both" count, and that's the only piece we were missing. Since either statement alone gives a single, definite answer ( 175 ), the answer is  D .

The takeaway for DS value questions: don't compute for its own sake - find the  one unknown  the question hinges on (here, the overlap), then ask whether each statement forces that unknown to a single value.

Answer: D

In a survey, voters were asked whether they approve or disapprove of

Prep Toolkit

Top 5 GMAT Debrief Videos

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

	B Approve	B Disapprove	B Neutral
A Approve	a	b	c	400
A Disapprove	d	e	f	400
A Neutral	g	h	i	200
	500	200	300	1000

GMAT Data Sufficiency (DS) Questions

In a survey, voters were asked whether they approve or disapprove of

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