# TANCET 2014 DS 77: Numbers

## 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:

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

## Question

Medium Data Sufficiency

Paul jogs at a constant rate for 80 minutes along the same route every day. How long is his route?

1. Statement 1: Yesterday, Paul began jogging at 5 p.m.
2. Statement 2: Yesterday, Paul had jogged 5 km by 5:40 p.m. and 8 km by 6:04 p.m.

Correct Answer    Choice (2). Statements (2) ALONE is SUFFICIENT.

## Explanatory Answer - step by step

• ### What should 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 "How long is his route?"

The answer to the question should be a number providing the distance of his route followed by a unit of distance viz., km, miles.

#### When is the data sufficient?

If we are able to come up with a unique value for the distance that Paul jogs, the data is sufficient.

If we are not able to come up with a unique answer – either we cannot find an answer at all or if we find more than one answer, the data is NOT sufficient.

#### What data is available from the question stem?

Paul jogs for 80 minutes at a constant rate along the same route every day.

• ### Statement (1) ALONE

#### Yesterday, Paul began jogging at 5 p.m.

All that we can determine is that Paul jogged till 6:20 p.m. yesterday.

With this information we cannot find the length of his route.

Statement (1) ALONE is NOT sufficient.

The moment we realize that statement (1) ALONE is NOT sufficient, we can narrow down our choices to 2 or 3 or 5.

To determine whether the answer is choice 2 or choice 3 or choice 5, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.

• ### Statement (2) ALONE

#### Yesterday, Paul had jogged 5 km by 5:40 p.m. and 8 km by 6:04 p.m.

Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said in statement (1) should not be used while evaluating statement (2).

Inference from statement 2: Between 5:40 and 6:04, Paul had covered a distance of 3 km in 24 minutes.

From question stem: Paul jogs 80 minutes every day and at a constant rate.

So, in 80 minutes Paul would have covered $$frac{3}{24}\\$ * 80 = 10 km. Using statement$2) we could get a UNIQUE answer.

Statement (2) ALONE is sufficient.

If statement (2) ALONE is SUFFICIENT and statement 1 ALONE is NOT sufficient, we can eliminate choices 3 and 5.

Hence, choice (2) is the answer.

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