TANCET 2011 Data Sufficiency Qn 1 - Speed Distance Time

Directions

The following problem has a question and two statements which are 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 on mathematics and every day facts, choose:

(1)    If you can get the answer from (1) ALONE but not from (2) alone
(2)    If you can get the answer from (2) ALONE but not from (1) alone
(3)    If you can get the answer from BOTH (1) and (2) TOGETHER, but not from (1) alone or (2) alone
(4)    If EITHER statement (1) ALONE or statement (2) ALONE suffices
(5)    If you CANNOT get the answer from statements (1) and (2) TOGETHER, but need even more data

Question

Plane X files at r miles per hour from A to B. Plane Y files at S miles per hour from B to A. Both planes take off at the same time. Which plane files at a faster rate? Town C is between A and B.
(1)    C is closer to A than it is to B
(2)    Plane X flies over C before plane Y

Correct Answer – Choice 5. Data is INSUFFICIENT

Explanatory answer

Information given in the question stem
1.    Plane X and Plane Y take off at the same time.
2.    Town C is between A and B.

Statement 1: C is closer to A than it is to B

This statement is not helpful in determining which of the two planes is faster unless we know that the two planes met at C. That is not stated in the statement or the question stem.

Statement 1 is INSUFFICIENT. 

Statement 2: Plane X flies over C before Plane Y

This statement alone is not sufficient to determine which of the planes is faster unless we know where C is located.

Statement 2 is INSUFFICIENT.

Combining the two statements, we know that C closer to A. X flies over C before Y.

Because C is closer to A, even if X is as fast as Y or even if it is slower than Y, X could have flown over C earlier than Y.

On the contrary if the statement had mentioned that Y flew over C before X and C is closer to A than to B, we could have inferred that Y was faster than X.

Even after using the two statements we cannot infer which plane is faster.

Choice 5 is the correct answer.