### Data-Sufficiency

Example-5

Question

Is n greater than 5?

(1) (n-5)(n-4)(n-3)>0

(2) n>3

Analysis

The first fact you should note is that it is not given that n is positive, nor is it given that n is an integer.

If Statement (1) alone is given, one possible value for n is 6, because the LHS is the inequality becomes 6*2*3 = 36 and is >0.

But Statement (1) will be true even if n =3.5 because, in this case two of the factors (n-5) and (n-4) will be negative, and (n-3) will be positive.

Therefore, by given Statement (1), n may be either >5 or <5.

So, Statement (1) alone does not help us to answer the question as YES or NO uniquely.

So, (A) is not the answer.

If Statement (2) alone is given, n can be equal to 3.5, 4.8, 1000 or any such number greater than 3. So, it may or may not be greater than 5.

So, Statement (2) alone does not help us to answer the question as YES or NO uniquely.

So, (B) is not the answer.

If both the Statements are taken together, n can again have either of the two values 3.5 or 6, and both of which will satisfy both the given statements. So, n may be <5 or >5.

So, both the statement together will not help us to answer the question as YES or No uniquely.

So, as per the instructions, (E) is the answer.