10% of GMAT test takers take the exam more than once and have a high

Question

10% of GMAT test takers take the exam more than once and have a high score of 650 or greater, and 20% of GMAT test takers who take the test only once have a score of 650 or greater. if 40% of GMAT test takers take the exam more than once, What percent of GMAT test takers have a high score of less than 650?

A. 10.5%

B. 22%

C. 30%

D. 70%

E. 78%

Show Answer

Official Answer

E

A. 10.5%

B. 22%

C. 30%

D. 70%

E. 78%

PyjamaScientist · Answer

Use a group grid to organize the information.

Let  total = 100 .

In the grids below:
-- All the numbers in the grid have to add up horizontally and vertically.
-- Values given by the problem are entered in   blue  .
-- Values calculated based upon information was given by the problem are entered in   red  .

40% take the exam more than once.
10% take the exam more than once and have a score of 700 or greater.

20% of GMAT test takers who take the test only once have a score of 700 or greater.

Total with a score less than 700 = 78%.

AnkitNandwani1 · Answer

To solve this problem, let's break down the given information and use basic probability concepts.

Given Data :

40% of GMAT test takers take the exam more than once. 
 60% of GMAT test takers take the exam only once (since 100% - 40% = 60%). 
 10% of test takers who take the exam more than once have a high score of 650 or greater. 
 20% of test takers who take the exam only once have a score of 650 or greater.   
  Definitions and Calculations :

Let P(M)P(M)P(M) represent the probability of taking the exam more than once. 
 Let P(O)P(O)P(O) represent the probability of taking the exam only once. 
 Let P(≥650∣M)P(	ext{≥650} | M)P(≥650∣M) represent the probability of scoring 650 or greater given the exam is taken more than once. 
 Let P(≥650∣O)P(	ext{≥650} | O)P(≥650∣O) represent the probability of scoring 650 or greater given the exam is taken only once.  
From the given data:

P(M)=0.40,P(O)=0.60P(M) = 0.40, \quad P(O) = 0.60P(M)=0.40,P(O)=0.60 P(≥650∣M)=0.10,P(≥650∣O)=0.20P(	ext{≥650} | M) = 0.10, \quad P(	ext{≥650} | O) = 0.20P(≥650∣M)=0.10,P(≥650∣O)=0.20 
  Total Probability of Scoring 650 or Greater : We use the law of total probability to find the overall probability of scoring 650 or greater:

P(≥650)=P(≥650∣M)⋅P(M)+P(≥650∣O)⋅P(O)P(	ext{≥650}) = P(	ext{≥650} | M) \cdot P(M) + P(	ext{≥650} | O) \cdot P(O)P(≥650)=P(≥650∣M)⋅P(M)+P(≥650∣O)⋅P(O)Substituting the values:

P(≥650)=(0.10⋅0.40)+(0.20⋅0.60)P(	ext{≥650}) = (0.10 \cdot 0.40) + (0.20 \cdot 0.60)P(≥650)=(0.10⋅0.40)+(0.20⋅0.60) P(≥650)=0.04+0.12=0.16P(	ext{≥650}) = 0.04 + 0.12 = 0.16P(≥650)=0.04+0.12=0.16 
  Probability of Scoring Less Than 650 : The probability of scoring less than 650 is the complement of the probability of scoring 650 or greater:

P(<650)=1−P(≥650)P(	ext{<650}) = 1 - P(	ext{≥650})P(<650)=1−P(≥650) P(<650)=1−0.16=0.84P(	ext{<650}) = 1 - 0.16 = 0.84P(<650)=1−0.16=0.84  
Thus, 84% of GMAT test takers have a high score of less than 650.

The answer is:  84%​

MBAApp27 · Answer

The answer above is incorrect, the answer should be 84%. You can apply weighted average here.

Krunaal · Answer

The answer 78% is correct. Not sure how weighted average would help here, the concept tested is of overlapping sets.

uks7 · Answer

Just one gotcha moment here : The language of question doesn't say that out of those who take the test more than once, 10% have score above 650. Instead it says out of all test takers who took GMAT, 10% scored above 650 & also have appeared more than once. 
Thus if total GMAT takers are 100, as per the question 10 got 650+ and also are among those who have taken the exam more than once. 
Next the question also gives out of 100, 40 have taken it more than once and a common pitfall is to take the 10% of this 40 and conclude that 4 student scored 650+ among the more than once group.

So with that out of the way, we have:
Total GMAT takers = 100
GMAT more than once count = 40
GMAT exactly once count = 60
GMAT more than once with 650+ = 10
GMAT exactly once with 650+ = 20% of 60 = 12 
Total % of 650+ = 10+12 = 22
=> Total % of less than 650 = 100-22 = 78

10% of GMAT test takers take the exam more than once and have a high

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