The task is to work out whether: 1. One or both of the statements alone is/are…

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The task is to work out whether:

1. One or both of the statements alone is/are sufficient for the question to be answered

2. The statements in isolation are useless but together they can solve the problem

3. Neither statement is of any use and the problem cannot be solved

The list of answer options are presented from A to E and are always the same.

If ‘n’ is a member of the set 16, 19, 21, 22, 24, 27, 36, 42 what is the value of ‘n’?

(1) ‘n’ is even

(2) ‘n’ is a multiple of 3

  1. A.

    Statement 1 alone is sufficient, but statement 2 alone is not sufficient

  2. B.

    Statement 2 alone is sufficient, but statement 1 alone is not sufficient

  3. C.

    Both statements together are sufficient, but neither statement alone is sufficient

  4. D.

    Each statement alone is sufficient

  5. E.

    Statements (1) and (2) together are not sufficient to answer the question asked, and additional data specific to the problem are needed

Attempted by 83 students.

Show answer & explanation

Correct answer: E

Concept: in a Data Sufficiency question, a statement (or a combination of statements) is sufficient only when it narrows the unknown down to exactly one value consistent with all the given data. If more than one candidate value remains after applying a statement (alone or combined with the other), that statement or combination is not sufficient. Evaluate statement (1) alone, then statement (2) alone, then both together, in that order.

  1. The given set is 16, 19, 21, 22, 24, 27, 36, 42, and n is some member of it.

  2. Statement (1) alone: 'n is even' restricts n to 16, 22, 24, 36, 42 - five values remain, so statement (1) alone is not sufficient.

  3. Statement (2) alone: 'n is a multiple of 3' restricts n to 21, 24, 27, 36, 42 - five values remain, so statement (2) alone is not sufficient.

  4. Combining both: n must be even AND a multiple of 3, i.e. a multiple of 6. Checking each member of the set gives 24, 36, 42 - three values remain, so even together the statements do not pin down a single value.

Cross-check: 24, 36 and 42 each independently satisfy both 'even' and 'multiple of 3', confirming three genuinely valid candidates survive combination, not one - so the sufficiency test fails at every stage, alone and together.

Since neither statement alone, nor both together, isolates a unique value of n, the correct classification is that statements (1) and (2) together are still not sufficient to answer the question.

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