TANCET 2014 DS Question 63: Number Properties
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:
 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
2. Positive and negative numbers 2 concepts
What is the value of x?
 Statement 1: x^{2} = 4.
 Statement 2: x < 0.
Correct Answer Choice (3). Both statements are needed to answer the question.
Explanatory Answer  step by step

What should we know from the Question Stem?
Before evaluating the two statements, answer the following questions to gain clarity.
What kind of an answer will the question fetch?
The question is "What is the value of x?"
The answer should be a number. It could be positive, negative, integer, noninteger, rational, irrational. Any number is good.
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 for x, the data is NOT sufficient.

Statement (1) ALONE
x^{2} = 4.
x may be 2 or x may be 2.
For both these values of x, x^{2} = 4.
We cannot find a UNIQUE value for x from the information given in statement (1).
Statement (1) ALONE is NOT sufficient.
The moment we realize that statement (1) is NOT sufficient, we can eliminate choices 1 and 4.
We can narrow down our choices to 2, 3 and 5.

Statement (2) ALONE
x < 0.
Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Do retain what was said in statement 1 in your mind.
We know that x is a negative number. x can take infinite values.
We cannot find a UNIQUE value for x from the information given in statement (2).
Statement (2) ALONE is NOT sufficient.
We can eliminate choice 2.
The answer narrows down to 3 or 5.

Combine the statements
1. x^{2} = 4.
+2. x < 0.
From statement (1) we can narrow down the values that x can take to exactly two possibilities. x could be +2 or 2.
From statement (2) we know that x is negative.
The only value of x that satisfies both the statements is 2.
Using statements (1) and (2) TOGETHER, we could find a unique answer for x.
Hence, the correct answer is Choice 3. Both statements are needed to answer the question.
Video Explanation
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