Question: In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?

1. 325
2. 1075
3. 1175
4. 2125
5. 2250

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

Using the probability formula we get the answer.

If 35 failed in A and 42 in B and 15 in both
Those failing in A or B but not in A and B is
P(Au(notB))+p((notA)uB)=p(a)+p(b)-2p(AnB)
=42+35-30
=47%
1175

Approach Solution 2:
100 = Percent failed one subject + Percent failed another subject – Percent failed both subjects + Percent failed neither subject
100 = 35 + 42 – 15 + P
100 = 62 + P
P = 38

We see that 38 percent of the candidates failed neither subject, i.e., 38 percent passed both subjects. Now we can use the following formula to find the number who passed either subject but not both:

Number who passed either subject but not both = number who passed only one subject + number who passed only another subject = (number who passed one subject – number who passed both subjects) + (number who passed another subject – number who passed both subjects)

N = 2500 x 0.65 – 2500 x 0.38 + 2500 x 0.58 – 2500 x 0.38
N = 2500 x (0.65 – 0.38 + 0.58 – 0.38)
N = 2500 x 0.47
N = 1175

Approach Solution 3:
This can be solved using Venn diagrams.

35% failed in one subject and 42% in another. 15% failed in both.

Below is the venn diagram representing the failures, in a sample of 100.

____________
______|_________
20% | 15% | 27% |
|_____ |________|
|
____________|

Obviously, those failing in one of the subjects = 20 + 27 = 47%

Total = 47% of 2500 = 1175.

“In an examination, 35% candidates failed in one subject and 42% failed”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book " The Official GMAT for Guide Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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