A study was conducted at four research universities on the number of f

Question

A study was conducted at four research universities on the number of female students and the number of students above 30 years of age in each of these universities. It is known that the total number of students, consisting of male and female students, is 8000. Wayward University has 40% of the total students, while the remaining three universities have the remaining number of students equally distributed amongst themselves.

The table below gives the number of female students and the number of students above 30 years of age as a percentage of the total number of students in each university.

University 
 Females 
 Age > 30 years 
 
  Vincent 
 60% 
 A 
 
  Kegol 
 55% 
 40% 
 
  MTI 
 30% 
 60% 
 
  Wayward 
 F 
 45% 
 
   Overall  
  45%  
  48%

From each drop down menu, select the option that creates the most accurate statement based on the information given above.

If 25% of the students above 30 years of age in Vincent University are females, then the number of males who are at most 30 years old in Vincent University is  GRAPH_1_PLACEHOLDER , which is approximately  GRAPH_2_PLACEHOLDER  percent of the total number of male students who are at most 30 years of age in all universities combined.

Shub1994 · Answer

Hi

As per calculations the answer for the first blank should be 40.

Bismuth83 · Answer

Thanks for checking! The answer should be updated now

Preksha_07 · Answer

Anyone who can answer?

MikeAdams · Answer

To solve the problem:
Total students in Vincent: 1600
Female students in Vincent: 60% of 1600 = 960
Students above 30 in Vincent: 50% of 1600 = 800
Female students above 30 in Vincent: 25% of 800 = 200
Male students at most 30 years old in Vincent: Total males (640) - Males above 30 (600) = 40
Thus, the number of males who are at most 30 years old in Vincent University is 40.

Best regard,

poojaarora1818 · Answer

Though, I have attempted it correctly. But it would be nice if you could provide an official explanation for it.

Bismuth83 · Answer

1. We are asked to  find the number of male students in Vincent University who are at most 30 years old  and  what percent is it compared to the total number of male students who are at most 30 years old in all universities .

2. Let’s first find A. From the text, we can conclude that all universities apart from Wayward have 20% of the total number of students. So:   
   0.2A + 0.2 * 40\% + 0.2 * 60\% + 0.4 * 45\% = 48\% \rightarrow A = \frac{48\% - 0.2 * 40\% - 0.2 * 60\% - 0.4 * 45\%}{0.2} = 50\% .

3. Now let’s draw a table for Vincent University, where we need to find x: 
 
    Vincent University  
  Male  
  Female  
 
    \leq 30   
  x  
  ?  
 
    > 30   
  ?  
  ?

4. The total number of students in Vincent University is  0.2 * 8000 = 1600 .  0.5 * 1600 = 800  students are above 30 and  0.25 * 800 = 200  are female. So, the other 600 are male. 
 
    Vincent University  
  Male  
  Female  
 
    \leq 30   
  x  
  ?  
 
    > 30   
  600  
  200

5.  0.6 * 1600 = 960  students are female and 960 - 200 = 760 students are female and less than 30.
 
    Vincent University  
  Male  
  Female  
 
    \leq 30   
  x  
  760  
 
    > 30   
  600  
  200

That means x = 1600 - (760 + 600 + 200) = 40.

6. The second part of our question is to find what percent is 40 compared to the total number of male students who are at most 30 years old in all universities.

7. This is impossible, since for all the universities, apart from Vincent, we are given information only about the female students or relating to the age 30 and not about both.

8. So, our answer is   40 and Cannot be determined  .

D3N0 · Answer

This question is good for practicing but no point in doing this much for the GMAT exam (IMO) 
It requires too much calculation at multiple levels.

SharonT · Answer

Thank you but can you please explain how you found this part of info "Students above 30 in Vincent: 50%". I was able to come up with the other info but I jammed on that part.

Bismuth83 · Answer

Let me try to explain it.

We need to find the value A. The overall percentage at the bottom of the column is the weighted average. Int the text it is said that: "Wayward University has 40% of the total students, while the remaining three universities have the remaining number of students equally distributed amongst themselves." This means that each university, other than Wayward, contributes 20% or 0.2. 
So, we can write the following equation:  0.2A + 0.2 * 40\% + 0.2 * 60\% + 0.4 * 45\% = 48\% \rightarrow A = \frac{48\% - 38\%}{0.2} = 50\% .

I hope that helped you!

SharonT · Answer

Yes it did! Thank you so much for explaining this.

A study was conducted at four research universities on the number of f

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University	Females	Age > 30 years
Vincent	60%	A
Kegol	55%	40%
MTI	30%	60%
Wayward	F	45%
Overall	45%	48%

Vincent University	Male	Female
\(\leq 30\)	x	?
\(> 30\)	?	?

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