In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?

(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.

(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'C'. Can you explain this answer?

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In an interview for a certain job, 120 candidates appeared and two que...

Steps 1&2: Understand question and draw inferences

Let the number of candidates who gave 0 correct answers, 1 correct answer and 2 correct answers = A, B and C respectively

A + B + C = 120 -----(1)

We have to find the value of A.

To do so, we need to find:

(i) Either the value of B and C

(ii) Or the value of (B + C)

Step 3: Analyze Statement 1

Number of students who answered at least one question correctly = B + C

We derive a relation between B and C, but we cannot find the value of B or C or (B + C) from equation (1) and (2).

INSUFFICIENT.

Step 4: Analyze Statement 2

Number of students who answered none or all questions correctly = A + C

We derive a relation between A and C, but we cannot find the value of B or C or (B + C) from equation (1) and (3).

Step 5: Analyze Statement 1 and Statement 2 together (if needed)

We have equations (1), (2) and (3) when we combine the two statements.

Substituting A and B from equation (2) and (3) in equation (1),

3C + 4C + C = 120

We can find the value of C from this equation and substitute the value in equation (3) the find the required value of A.

SUFFICIENT.

(C) is the correct answer.

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In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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