TANCET 2014 DS Qn 80: Number Properties

Directions for TANCET Data Sufficiency Questions

The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:

Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
Choice 4 if each statement ALONE is sufficient.
Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

Question

Hard Data Sufficiency

If t is a multiple of prime number s, is t a multiple of s²?

Statement 1: s < 4
Statement 2: t = 18

Correct Answer Choice (5). Statements (1) and (2) TOGETHER are not sufficient.

Explanatory Answer - step by step

Question Statement (1) Alone Statement (2) Alone Statements Together Tabs

What do we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

What kind of an answer will the question fetch?

The question is "Is t a multiple of s²?"

The answer to an “is” question should be “yes” or “no”.

When is the data sufficient?

If we are able to come up with a CONCLUSIVE answer – a DEFINITE YES or a DEFINITE NO, the data is sufficient.

If we are not able to come up with a DEFINITE answer – if we find that for some values t is a multiple of s² and for other values it is not, the data is NOT sufficient.
Statement (1) ALONE

s < 4

Approach: Look for a counter example.

Example: t = 12 and s = 2 (question stem states that s is a prime number);

s² = 4. 't' is a multiple of s²

Answer to question with these values: YES

Counter Example: t = 12 and s = 3 (question stem states that s is a prime number);

s² = 9. 't' is NOT a multiple of s²

Answer to question with these values: NO

A counter example exists. So, statement (1) does not provide us with a DEFINITE YES or NO.

Statement (1) ALONE is NOT sufficient.

If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.

Choices narrow down to 2, 3, or 5.
Statement (2) ALONE

t = 18.

Approach: Look for a counter example.

Example: t = 18 and s = 3 (question stem states that s is a prime number);

s² = 9. 't' is a multiple of s²

Answer to question with these values: YES

Counter Example: t = 18 and s = 2 (question stem states that s is a prime number);

s² = 4. 't' is NOT a multiple of s²

Answer to question with these values: NO

A counter example exists. So, statement (2) does not provide us with a DEFINITE YES or NO.

Statement (2) ALONE is NOT sufficient.

If statement (2) ALONE is NOT sufficient, we can eliminate choice 2 as well.

Choices narrow down to 3 or 5.
Statements Together

1. s < 4.
+

2. t = 18.

Approach: Look for a counter example.

Example: t = 18 and s = 3 (question stem states that s is a prime number);

s² = 9. 't' is a multiple of s²

Answer to question with these values: YES

Counter Example: t = 18 and s = 2 (question stem states that s is a prime number);

s² = 4. 't' is NOT a multiple of s²

Answer to question with these values: NO

A counter example exists. Statements together do not provide us with a DEFINITE YES or NO.

Despite using statements (1) and (2) together we could NOT determine the answer to the question.

Hence, Choice (5) is the answer.