TANCET 2014 DS Q75 : Simple Equations

Directions for TANCET Data Suficiency 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

Very Easy Data Sufficiency

If a - b = c, what is the value of b?

Statement 1: c + 6 = a
Statement 2: a = 6

Correct Answer Choice (1). Statement (1) ALONE is sufficient; Statement (2) is NOT 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 b?"

The answer to should be a number. For e.g., b = 12.

When is the data sufficient?

If we are able to come up with a UNIQUE answer for the value of b, the data is sufficient.

If we are not able to come up with a UNIQUE value for b, the data is NOT sufficient.

What data do we know from the question stem?

An equation with a relation between a, b and c. a – b = c.

We can rewrite the same as b = a – c.
Statement (1) ALONE

c + 6 = a

i.e., a – c = 6.

We know that b = a – c. Therefore, b = 6.

We could get a UNIQUE answer to the question with statement 1.

Statement (1) ALONE is sufficient.

If statement (1) ALONE is sufficient, we can narrow our choices to 1 or 4.
Statement (2) ALONE

a = 6

From the question stem we know b = a – c

So, b = 6 – c.

Without knowing the value of c, we cannot find the value of b.

Using statement (2) ALONE we could NOT get a UNIQUE answer to the question.

Statement (2) ALONE is NOT sufficient.

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

Hence, choice (1) is the answer.