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
If t is a multiple of prime number s, is t a multiple of s^{2}?
 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

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 s^{2}?"
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 s^{2} 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);
s^{2} = 4. 't' is a multiple of s^{2}
Answer to question with these values: YES
Counter Example: t = 12 and s = 3 (question stem states that s is a prime number);
s^{2} = 9. 't' is NOT a multiple of s^{2}
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);
s^{2} = 9. 't' is a multiple of s^{2}
Answer to question with these values: YES
Counter Example: t = 18 and s = 2 (question stem states that s is a prime number);
s^{2} = 4. 't' is NOT a multiple of s^{2}
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);
s^{2} = 9. 't' is a multiple of s^{2}
Answer to question with these values: YES
Counter Example: t = 18 and s = 2 (question stem states that s is a prime number);
s^{2} = 4. 't' is NOT a multiple of s^{2}
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.
Video Explanation
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XAT TANCET Practice Questions  Listed Topic wise
 Number Theory
 Permutation Combination
 Probability
 Inequalities
 Geometry
 Coordinate Geometry
 Mensuration
 Trigonometry
 Data Sufficiency
 Percentages
 Profit Loss
 Ratio Proportion
 Mixtures & Alligation
 Speed Distance & Time
 Pipes, Cisterns & Work, Time
 Simple & Compound Interest
 Races
 Averages & Statistics
 Progressions : AP, GP & HP
 Set Theory
 Clocks Calendars
 Linear & Quadratic Equations
 Functions
 English Grammar
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