A certain number of people were polled to determine which of three

Question

A certain number of people were polled to determine which of three desserts they enjoyed: cupcakes, apple pie, and ice cream sundaes. If everyone polled enjoyed at least one of the three desserts, what fraction of the people polled enjoyed exactly two desserts?

(1) 1/3 of the people polled enjoyed cupcakes, 1/2 enjoyed apple pie, and 3/4 enjoyed ice cream sundaes.
(2) 1/4 of the people polled enjoyed all three desserts.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

walterwhite756 · Answer

Assume number of people = 12.

Stmt (1): 1/3 (=4) of the people polled enjoyed cupcakes, 1/2 (=6) enjoyed apple pie, and 3/4 (=9) enjoyed ice cream sundaes.
We can't find exactly 2 from this information.  INSUFFICIENT

Stmt (2): 1/4 (=3) of the people polled enjoyed all three desserts.
We can't find exactly 2 from this information.  INSUFFICIENT

Stmt (1) and Stmt (2): Apply following formula, CC = cupcakes, AP = apple pies, ICS = ice cream sundaes
 Total = CC + AP + ICS - (Exactly 2 groups) - 2 (Exactly 3 groups) + None

Since none = 0, We have only one unknown and hence solvable.  SUFFICIENT

Therefore  C is the answer.

Hope it helped.

zhanbo · Answer

(1) Only
Supposing there are a total of 12 people
4 enjoyed cupcakes
6 enjoyed apple pie
9 enjoyed ice cream sundaes
It is possible that 4 people enjoyed all three
Then nobody enjoys cupcakes only, or both cupcakes and apple pie, or both cupcakes and ice cream sundaes.
Even in this rather extreme case, the number of people who enjoy both pie and ice cream sundaes can be 0, 1, or 2. 
Not sufficient

(2) Only
Evidently insufficient.

(1)(2) Together
fraction of the people polled enjoyed exactly two desserts 
= 1/3 + 1/2 + 3/4 - 2*(1/4) - 1
Sufficient

The answer is thus  (C) .

8.toastcrunch · Answer

To solve for any one variable in this equation, we need at least three of the others, so neither Statement (1) nor Statement (2) is sufficient on its own, as each provides only one variable. Taking the two together, we may find it easier to see what info we have by picking numbers, so let's say 12 people were polled. Statement (1) would then tell us that 4 people like cupcakes, 6 like apple pie, and 9 like ice cream sundaes, so our Total is 4+6+9 = 19. Statement (2) tells us that our double overlap - the people in the intersection of all three circles is 3 (1/4 of 12). Now we can plug into our equation: 19- (2 * 3) - (sum of single overlaps) = 12. This tells us that exactly one person is in the single overlaps - the people who liked exactly one of the two things so we have a single value.

Answer is C

Answer is C

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

A certain number of people were polled to determine which of three

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

GMAT Data Sufficiency (DS) Questions

A certain number of people were polled to determine which of three

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