### Data-Sufficiency

Example-4

Data-Sufficiency section often features equations or inequalities involving algebraic quantities x, y, z, a, b, c etc… representing numbers and their properties.

Most of them can be answered by plugging in specific values for the algebraic quantities in the given equations or inequalities and testing their values.

Question

If b is the product of two consecutive positive integers, is b divisible by 6?

(1) b is divisible by 4

(2) b is divisible by 3

Analysis

Questions, like this, can be answered by giving specific values to the unknown quantities consistent with the given conditions.

The given condition is that b is the product of two consecutive positive integers.

Let us consider pairs of consecutive positive integers (1,2), (2,3), (3,4), (4,5), (5,6) and (6,7). Their products are 2, 6, 12, 20, 20, 30 and 42. And b may represent any of them.

Statement (1) says that b is divisible by 4. Among the possible values (2, 6, 12, 20, 20, 30 and 42) of b, only the numbers 12 and 20 are divisible by 4. Of these two numbers, while 12 is divisible by 6, 20 is not divisible by 6.

So, the question can be answered by the Statement (1) alone.

So, (A) is not the answer.

Statement (2) says b is divisible by 3. Among the possible values (2, 6, 12, 20, 30 and 42) of b, the numbers 6, 12, 30 and 42 are divisible by 3. We can easily see that each of them is divisible by 6 also.

So, from (2) alone, we can answer the question as YES.