40 people admitted to a certain graduate program had taken the TOEFL

Question

40 people admitted to a certain graduate program had taken the TOEFL and 35 had taken the GRE. Were more than 60 people admitted to the program ?

(1) 1/5 of the people admitted to the program had taken both the TOEFL and the GRE.
(2) More than 20 of the people admitted to the program had not taken either the TOEFL or the GRE.

yuvrajbhama · Answer

Hi can anyone expain this quetsion?
I choose C, coz if toefl and gre we take common 35 is the overlap, so with statement 1 20% had both ie. 35 admits, so 5* 35 will make the 100% which will be more then 60:- 1 is sufficient. 
statement 2: 40 being the number of people in toefl more the 20 are with non i.e. torfl and gre makeing 40+ 21(more then 20) is also sufficient.

arushi118 · Answer

Using Statement 2:
    
 T 
 not T 
 Total 
 
  G

35 
 
  not G 
  
 >20

Total 
 40 
 >20 
 x

total will be: 40 + >20 -> this will be more than 60.
So sufficient with only statement 2. But not sure how is statement 1 also sufficient.

dianyang · Answer

i chose B and don't understand why D is correct :<

Vivek1707 · Answer

As per statement 1

T 
 ~T 
 Total 
 
  GRE 
 1/5x 
  
 35 
 
  ~GRE

Total 
 40 
  
 x

Now notice that x has to be more then 40 and since you dealing with people, it has to be an integer.

Now if you pick number divisible by 5 more than 40 such as 45, 50, 55, 60 and plug them to the cell of T and GRE both (i.e the top left cell), it wont work unless the value of x is more than 60

Eg if you take x = 45, then 1/5x = 9 so the table would look like this

T 
 ~T 
 Total 
 
  GRE 
 9 
 26 
 35 
 
  ~GRE 
 31

Total 
 40 
  
 x

Notice that even if ~GRE and ~T are 0, 26 from ~T will flow down to the last row and the total will need to be 66. So this wont work.

None of the values below or equal to 60 will work in that case hence A is sufficient.

Statement 2 is anyways sufficient since if ~T and ~GRE is more than 20, i.e if say its 21 if the ~T and GRE cell is 0 then 21 + 40 = 61 would be the minimum total

Hence: Answer is D
 
Key take away: When dealing with DS quesitons involving sets, be careful about what is the max number that can be put in any of the cells. Often DS traps are hidden in those aspects.

kevincan · Answer

Regarding (1): If n is the number of students , n/5 have taken both exams , so we can write

n >= 40 + 35 - n/5 , ( greater than or equal as there may be students who have taken neither exam)

Thus 6n / 5 >= 75

n > = 375/6 > 60

Alternatively, as 45+ 30 = 75, there are 60 or fewer students in total only if the number students who have taken both exams is at least 15. But since 20 percent (i.e. 1/5 ) of the students have taken both exams , if there are at least 15 students who have taken both exams , there would be at least 75 ( 15 times 5) students in total. Thus it is impossible that they are 60 or fewer students .

totamofficiis · Answer

Do not understand why D is correct. 
Set T all the students given TOEFL, Set G all the student Given GRE. Assuming U == (P u G)
I need to answer if (T u G) > 60
T=40
G=35
Statement 1. (T ^ G) = 1/5 *(T u G) ==> T+G = 6/5 (T u G) hence can answer.
Statement 2 (not T u not G) > 20 ==> not (T ^ G ) === (T u G) - (T^G) > 20. now T- (T^G) + G - (T^G) > 20 => 75-20 > 2(T^G) 
=> so T^G <= 27
T+G - (T^G)>= 40+35-27 =>75-27 => 48 So i can not answer from statement B.

kevincan · Answer

U == (P u G)

What does this mean ?
I think you’re forgetting the students may not have taken either of the two exams

Dereno · Answer

Let us consider a two set vent diagram, where 40 denote the circle representing TOFEL.

And, 35 denote the circle representing GRE.

Let x denote the common overlapping region. And d = none.

We need to find is the total (T) more than 60 ?

Statement 1:

1/5 of the people admitted to the program had taken both the TOEFL and the GRE.

If we sum all the individual parts of the set 40-x + x + 35-x + none = T

75 - x + none = T

Given that x = (1/5)T

75 + none = (6/5)T

Even if none =0.

T = (75*5)/6 = 62.5 > 60.

Hence,  Sufficient

Statement 2:

More than 20 of the people admitted to the program had not taken either the TOEFL or the GRE.

75 - x + none = T

Given that none = greater than 20.

(Greater than 95 )- x = T

What is the maximum value the overlapping part can take ? 35 = x.

Greater than 60 = T

Hence,  Sufficient

Option D

totamofficiis · Answer

yes my logic is wrong and i can prove it is wrong though the student might not have taken either of the exam was the issue.

-P u -G expansion was wrong. sorry. I got confused.

40 people admitted to a certain graduate program had taken the TOEFL

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GMAT Data Sufficiency (DS) Questions

40 people admitted to a certain graduate program had taken the TOEFL

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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