In a batch of 150 candidates applying for a training program, 90 are graduates and 100 know programming.

Consider the following statements:
Statement I: The maximum possible number of graduates who know programming is 90.
Statement II: The minimum possible number of graduates who know programming is 50.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

In a batch of 150 candidates applying for a training program, 90 are graduates and 100 know programming.

Consider the following statements:
Statement I: The maximum possible number of graduates who know programming is 90.
Statement II: The minimum possible number of graduates who know programming is 50.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

Let G be graduates, P be those who know programming.
Total = 150, G = 90 and P=100

Maximum possible overlap (graduates who know programming)
= Minimum of (graduates, programmers) = min (90, 100) = 90

Minimum possible overlap
= G + P &minus; Total = 90 + 100 &minus; 150 = 40

So:

Statement I: Maximum number is 90 &rarr; Correct

Statement II: Minimum number is 40 &rarr; Incorrect

Hence, option a is correct.

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