# TANCET 2014 DS 65: Numbers

## Directions

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

Easy Data Sufficiency

Manju purchased 18 cans of soda, some of which contained diet soda. How many of the cans did not contain diet soda?

1. Statement 1: Of the cans Manju purchased, the number containing diet soda is equal to the number not containing diet soda.
2. Statement 2: Of the cans Manju purchased, the number of cans containing diet soda is odd.

Correct Answer    Choice (1). Statement (1) 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 many of the cans did not contain diet soda?"

The answer should give the number of cans. i.e., the answer is essentially a number less than or equal to 18.

#### When is the data sufficient?

If we are able to come up with a unique value for the number of cans that do not contain diet soda, the data is sufficient.

If we are not able to come up with a unique answer for the number of cans that do not contain diet soda, the data is NOT sufficient.

• ### Statement (1) ALONE

#### Of the cans Manju purchased, the number containing diet soda is equal to the number not containing diet soda.

From the question stem we know that Manju purchased 18 cans.

If the number of cans containing diet soda is equal to the number not containing diet soda, we can deduce that 9 cans do not contain diet soda.

We could find a UNIQUE answer using statement (1) ALONE.

Statement (1) ALONE is sufficient.

The moment we realize that statement (1) is sufficient, we can narrow down our choices to 1 or 4.

To determine whether the answer is choice 1 or choice 4, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.

• ### Statement (2) ALONE

#### Of the cans Manju purchased, the number of cans containing diet soda is odd.

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

The number of cans containing diet soda is odd. The number could be 1 or 3 or 5 or any odd number up to 17.

Correspondingly, the number of cans not containing diet soda will be an odd number down from 17 to 1.

We cannot find a UNIQUE value for the number of cans not containing diet soda from the information given in statement (2).

Statement (2) ALONE is NOT sufficient. Hence, choice (1) is the answer.

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