In a class of 100 students, how many boys got distinction in an examination, if all of them took the exam?1. Exactly 20 girls got distinction in the examination.2. 3/5 of the class got a distinction in the examinationa.Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question asked.b.BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientc.EACH statement ALONE is sufficient to answer the question asked.d.Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.e.Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question asked.
Question
In a class of 100 students, how many boys got distinction in an examination, if all of them took the exam?1. Exactly 20 girls got distinction in the examination.2. 3/5 of the class got a distinction in the examinationa.Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question asked.b.BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientc.EACH statement ALONE is sufficient to answer the question asked.d.Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.e.Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question asked.
Solution
The answer is b. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
Here's why:
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Statement 1 tells us that 20 girls got distinction. However, it doesn't tell us anything about how many boys there are or how many of them got distinction.
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Statement 2 tells us that 60 students (3/5 of 100) got distinction. However, it doesn't tell us how many of these are boys.
When we combine both statements, we know that 60 students got distinction and 20 of them are girls. Therefore, the remaining 40 students who got distinction must be boys. So, 40 boys got distinction in the examination.
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