GMAT CLUB OLYMPICS: In a survey of an Olympic team members, 1/6th of

Question

In a survey of an Olympic team members, 1/6th of them said they do not watch movies during their free time, of those, 3/4th said they also do not play video games during their free time. Is the number of the Olympic team members who do not play video games equal to 90 ?

(1) 210 members of the Olympic team said that they watch movies and play video games during their free time
(2) 15 members of the Olympic team said that they play video games but do not watch movies during their free time

M36-14

Bunuel · Accepted Answer

Official Solution:

In a survey of an Olympic team members,  \frac{1}{6}^{th}  of them said they do not watch movies during their free time, of those,  \frac{3}{4}^{th}  said they also do not play video games during their free time. Is the number of the Olympic team members who do not play video games equal to 90 ?

This is what we know from the stem:

https://gmatclub.com/tests-beta/resources/import/img/M36-14%20Stem.png

The question asks whether YELLOW box is 90. (1) 210 members of the Olympic team said that they watch movies and play video games during their free time
 
Fill the matrix with the information provided in this statement:

https://gmatclub.com/tests-beta/resources/import/img/M36-14%20Statement%201.png

So, the question asks whether  x - (210 + \frac{x}{24})  is 90. Solving  x - (210 + \frac{x}{24})=90  gives  x = \frac{7200}{23} , which is not possible because  x  represents the number of people and must be an integer. Therefore, the number of the Olympic team members who do not play video games cannot equal to 90. Sufficient. (2) 15 members of the Olympic team said that they play video games but do not watch movies during their free time

Fill the matrix with the information provided in this statement:

https://gmatclub.com/tests-beta/resources/import/img/M36-14%20Statement%202.png

From this statement we get that  \frac{x}{24} = 15 , which gives  x  as 360. So, we get

https://gmatclub.com/tests-beta/resources/import/img/M36-14%20Statement%202+.png

As you can see there is no way to tell whether the yellow box is 90 or not. Not sufficient.

Answer: A

Kinshook · Answer

Given: In a survey of an Olympic team members, 1/6th of them said they do not watch movies during their free time, of those, 3/4th said they also do not play video games during their free time.

Asked: Is the number of the Olympic team members who do not play video games equal to 90 ?

Watch movies  ~Watch movies  Total  
  Play video games      x/4  
  ~Play video games      Is  3x/4  = 90? 
  Total  5x/6  x/6  x

(1) 210 members of the Olympic team said that they watch movies and play video games during their free time
 
    Watch movies  ~Watch movies  Total  
  Play video games  210    x/4>210  
  ~Play video games       3x/4   
  Total  5x/6  x/6  x  
 
Surely, the Olympic team members who do not play video games = 3x/4 > 3*210 = 630 and NOT equal 90.
SUFFICIENT

(2) 15 members of the Olympic team said that they play video games but do not watch movies during their free time
 
    Watch movies  ~Watch movies  Total  
  Play video games    15  x/4> 15  
  ~Play video games      Is  3x/4  = 90? 
  Total  5x/6  x/6  x  
 
the Olympic team members who do not play video games = 3x/4 > 3*15 = 60
Which may or may not be equal to 90
NOT SUFFICIENT

IMO A

cs15811581 · Answer

In a survey of an Olympic team members, 1/6th of them said they do not watch movies during their free time, of those, 3/4th said they also do not play video games during their free time. Is the number of the Olympic team members who do not play video games equal to 90 ?

Let us fill up the data in 2*2 matrix

M  NM  Total  
  v     \frac{x}{24}     
  NV  y   \frac{x}{8}     
  Total   \frac{5x}{6}    \frac{x}{6}   x

We have to answer: Is  y+\frac{x}{8}=90 ?

(1) 210 members of the Olympic team said that they watch movies and play video games during their free time

M  NM  Total  
  V  210   \frac{x}{24}     
  NV  y   \frac{x}{8}     
  Total   \frac{5x}{6}    \frac{x}{6}   x

210+y=\frac{5x}{6}…….y=\frac{5x}{6}-210 .
Thus,  y+\frac{x}{8}=\frac{5x}{6}-210+\frac{x}{8}=\frac{23x}{24}-210 
Can  \frac{23x}{24}-210=90…….\frac{23x}{24}=300……x=\frac{300*24}{23} .
NO, as x will not be an integer. 
Sufficient

(2) 15 members of the Olympic team said that they play video games but do not watch movies during their free time
 
    M  NM  Total  
  V     \frac{x}{24}=15     
  NV  y   \frac{x}{8}     
  Total   \frac{5x}{6}    \frac{x}{6}   x  
 
So we get  \frac{x}{24}=15…..x=360 
 \frac{x}{8}=\frac{360}{8}=45 
Is y+45=90?

Yes and no both as y can take values such as 45, 46, 50 etc
Insufficient

A

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	Watch movies	~Watch movies	Total
Play video games			x/4
~Play video games			Is 3x/4
Total	5x/6	x/6	x

	M	NM	Total
v		\(\frac{x}{24}\)
NV	y	\(\frac{x}{8}\)
Total	\(\frac{5x}{6}\)	\(\frac{x}{6}\)	x

	M	NM	Total
V		\(\frac{x}{24}=15\)
NV	y	\(\frac{x}{8}\)
Total	\(\frac{5x}{6}\)	\(\frac{x}{6}\)	x

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GMAT CLUB OLYMPICS: In a survey of an Olympic team members, 1/6th of

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