M40-67

Question

Out of 25 Gryffindor students, 16 play chess, and 11 play Quidditch. How many Gryffindor students play both chess and Quidditch?

(1) Three Gryffindor students play neither chess nor Quidditch.
 
(2) For every three Gryffindor students who play neither chess nor Quidditch, there are five Gryffindor students who play both chess and Quidditch.

Bunuel · Answer

Official Solution:

Out of 25 Gryffindor students, 16 play chess, and 11 play Quidditch. How many Gryffindor students play both chess and Quidditch? 
 
We are given that:
   
{Total} = {Chess} + {Quidditch} - {Both} + {Neither}
 
25 = 16 + 11 - {Both} + {Neither}
 
{Both} = 2 + {Neither}
   
(1) Three Gryffindor students play neither chess nor Quidditch.
 
This gives {Neither} = 3. Thus, {Both} = 2 + {Neither} = 2 + 3 = 5. Sufficient.
 
(2) For every three Gryffindor students who play neither chess nor Quidditch, there are five Gryffindor students who play both chess and Quidditch.
 
This implies that {Neither} : {Both} = 3 : 5, which gives  {Neither} = \frac{3}{5} * {Both} . Substituting this into {Both} = 2 + {Neither}, we get a linear equation with one unknown, {Both}, hence we can solve for it. Sufficient.

Answer: D

MT1302 · Answer

Hello  Bunuel ,

Can you explain 2nd statement in a more elaborate way ?

What I have understood is :

Let Neither be  X,  so for every  \frac{X}{3}  students there are Both =  \frac{5X}{3 }  .

But I am getting value of x in fraction.

Bunuel · Answer

{Both} = 2 + {Neither}

5x/3 = 2 + x

5x = 6 + 3x

2x = 6

x = 3

{Both} = 2 + {Neither} = 2 + 3 = 5.

Vikramaditya00 · Answer

Is both = 2+neither a fromula for such questions, if not how did we take two for solving this question

Bunuel · Answer

The formula for two overlqapping groups is {Total} = {Group 1} + {Group 2} - {Both} + {Neitrher}. From the stem we get:

{Total} = {Chess} + {Quidditch} - {Both} + {Neither}

25 = 16 + 11 - {Both} + {Neither}

{Both} = 2 + {Neither}

(2) says that {Neither} : {Both} = 3 : 5, which gives  {Neither} = \frac{3}{5} * {Both} . Substituting this into {Both} = 2 + {Neither}, we get a linear equation with one unknown, {Both}, hence  we can solve for it .

pc343 · Answer

hi, great question.

it might be a personal problem but i can never get the answer choices to pop up, whether its on the email or on the website. any idea what could be happening here?

in this case i only see the following:

Out of 25 Gryffindor students, 16 play chess, and 11 play Quidditch. How many Gryffindor students play both chess and Quidditch?

(1) Three Gryffindor students play neither chess nor Quidditch.

(2) For every three Gryffindor students who play neither chess nor Quidditch, there are five Gryffindor students who play both chess and Quidditch.

And then the show answer button

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

pc343 · Answer

great, thank you for the clarification

rdsab · Answer

in the statement B, suppose only chess=6, only quidditch=1, then both chess and quidditch=10 and neither=6. similarly, chess only =11, only quidditch=6 and both =5, neither =3. the ratio remains same for neither and both. Hence, answer should be A

Bunuel · Answer

The answer should be, and is, D. You're overlooking the fact that the total number of students must be 25. Your first example doesn't satisfy this condition, which is why your reasoning is incorrect.

rdsab · Answer

yes thanks Bunuel. i checked again and the answernis indeed D. My firs equation doe not add up to 25. thank you for the clarification. I overthought this one:(

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.

M40-67

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