M36-14

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:



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:



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:



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



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


Answer: A