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16 Jun 2022, 19:30
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A
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Difficulty:
25%
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Question Stats:
79% (01:56) correct
21%
(02:35)
wrong
based on 42
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The average of marks obtained by 120 candidates in a certain examination is 33. If the average marks of passed candidates is 37 and that of the failed candidates is 13, what is the number of candidates who passed the examination ?
(A) 100
(B) 105
(C) 110
(D) 115
(E) 120
(A) 100
(B) 105
(C) 110
(D) 115
(E) 120
16 Jun 2022, 22:27
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We can solve this question using the formula: Average = Sum/No. of values
33 = Sum of marks of 120 candidates/120
Sum of marks of 120 candidates (Let this be S1) = 3960 (i.e. 33*120) ----- Equation 1
Let the no. of candidates who passed = X
Thus, no. of candidates who failed will be = 120 - X
We know that the average marks of candidates who passed = 37
Using the same average formula we can say that,
37 = Sum of candidates who passed (Let this be SP) /X
37X = SP ---- Equation 2
We know that the average marks of candidates who failed = 13
Using the same average formula we can say that,
13 = Sum of candidates who failed (Let this be SF) / (120-X)
13(120-X) = SF ----- Equation 3
Further, Sum of marks of 120 candidates = Sum of candidates who passed + Sum of candidates who failed, i.e. S1 = SP + SF
From equation 1, 2 and 3 we can say,
37X + 13(120-X) = 3960
24X = 2400
X = 100
The number of candidates that passed = 100
Answer choice (A)
33 = Sum of marks of 120 candidates/120
Sum of marks of 120 candidates (Let this be S1) = 3960 (i.e. 33*120) ----- Equation 1
Let the no. of candidates who passed = X
Thus, no. of candidates who failed will be = 120 - X
We know that the average marks of candidates who passed = 37
Using the same average formula we can say that,
37 = Sum of candidates who passed (Let this be SP) /X
37X = SP ---- Equation 2
We know that the average marks of candidates who failed = 13
Using the same average formula we can say that,
13 = Sum of candidates who failed (Let this be SF) / (120-X)
13(120-X) = SF ----- Equation 3
Further, Sum of marks of 120 candidates = Sum of candidates who passed + Sum of candidates who failed, i.e. S1 = SP + SF
From equation 1, 2 and 3 we can say,
37X + 13(120-X) = 3960
24X = 2400
X = 100
The number of candidates that passed = 100
Answer choice (A)
wadhwakaran
Joined: 31 Mar 2022
Last visit: 22 Jul 2025
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Location: India
Concentration: General Management, International Business
Schools: INSEAD Aug'24 intake Oxford Said'25 Judge '25 Imperial'25 HEC Sep'24 Intake LBS '26 ISB '27
GMAT 1: 700 Q50 V35
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Schools: INSEAD Aug'24 intake Oxford Said'25 Judge '25 Imperial'25 HEC Sep'24 Intake LBS '26 ISB '27
GMAT 1: 700 Q50 V35
Posts: 260
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16 Jun 2022, 22:33
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use concept of allegations in this question
passed failed
37 13
33 (total)
20 4
Therefore, ratio of pass to fail students is 5:1
meaning that out of very 6 students, 5 passed the test and 1 failed
therefore, out of 120, 100 students passed the test
passed failed
37 13
33 (total)
20 4
Therefore, ratio of pass to fail students is 5:1
meaning that out of very 6 students, 5 passed the test and 1 failed
therefore, out of 120, 100 students passed the test
