### Data-Sufficiency

Example-3

Question

If x and y are prime numbers, is x(y-6) odd?

(1) y > 10

(2) x < 3

Analysis

You must remember that (i) all the prime numbers are positive, (ii) the only even prime number is 2 and (iii) all other prime numbers are odd.

You must also remember that, by definition, 1 is not considered a prime number.

For the product of two numbers to be odd, each of the numbers must be odd.

If Statement (1) alone is given, y mat have any of the values 11, 13, 17, 19, 23 … all of which are prime numbers and odd. In these cases, (y-6) will have the values 5, 7, 11, 13, 17 respectively, all of which are also odd.

Since no in formation has been given in Statement (1) about x, it can have any of the values 2, 3, 5, 7, 11, 13, 17, 19, 23 etc. The product x(y-6) will be even if x=2, and will be odd for all other values of x. So, without knowing whether x-2 or not, the question can be answered either YES or NO uniquely.

So, (A) is not the answer.

If statement (2) alone is given, the only possible value for x is 2. Therefore the product x(y-6) becomes 2(y-6), which will be an even number for all values of y.

So, from Statement (2) alone, we can answer the question (Is x(y-6) odd?) as NO.

Because this is an unambiguous answer, we must conclude that Statement (2) by itself helps us to answer the question, and must therefore choose (B) as the answer.