TANCET 2014 DS 78: 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:

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

Easy Data Sufficiency

What is the value of the integer x?

Statement 1: x = \\sqrt[3]{64}\\)
Statement 2: x² = 2x + 8

Correct Answer Choice (1). Statements (1) ALONE is SUFFICIENT.

Explanatory Answer - step by step

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

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 "What is the value of integer x?"

The answer to the question should be a number, an integer value for x.

When is the data sufficient?

If we are able to come up with a unique value for x, 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?

We know that x is an integer.
Statement (1) ALONE

x = \\sqrt[3]{64}\\)

Therefore, x = 4.

We are able to find an UNIQUE value for x using data in statement 1.

Statement (1) ALONE is sufficient.

The moment we realize that statement (1) ALONE 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

x² = 2x + 8

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

Rewriting the expression results in the quadratic equation x² - 2x – 8 = 0

Factorize the quadratic equation: (x- 4)(x + 2) = 0

So, x is either 4 or x is -2.

Both are integers. So, x could take either of these values.

Using statement (2) we could not get a UNIQUE answer.

Statement (2) ALONE is NOT sufficient.

If statement (1) ALONE is SUFFICIENT and statement 2 ALONE is NOT sufficient, we can eliminate choices 4.

Hence, choice (1) is the answer.