Explanation

Statement (1)

We can quickly test this out with a few numbers. If xy = 5 × 10 = 50, then the population grew by 5% and then 10 %. 105% × 110% ≈ 116% growth. On the other hand, if xy = 1 × 50 = 50, then the population grew a total of 101% × 150% ≈ 151%.

This statement is clearly insufficient. The answer must be B, C, or E.

Statement (2)

This statement is very specific; there’s probably a reason for it. If we wanted to calculate the total percent increase in the population over both years, it would look like this:

(100+x)% × (100+y)%.

If we expand the whole equation (dropping the percentage signs, which we can add back later), it will look like this:

10000+100x+100y+xy. In other words, statement (2) gives us exactly the variables we need to solve the total percentage increase.

This statement is sufficient.

**The correct answer is B.**

We can quickly test this out with a few numbers. If xy = 5 × 10 = 50, then the population grew by 5% and then 10 %. 105% × 110% ≈ 116% growth. On the other hand, if xy = 1 × 50 = 50, then the population grew a total of 101% × 150% ≈ 151%.

This statement is clearly insufficient. The answer must be B, C, or E.

Statement (2)

This statement is very specific; there’s probably a reason for it. If we wanted to calculate the total percent increase in the population over both years, it would look like this:

(100+x)% × (100+y)%.

If we expand the whole equation (dropping the percentage signs, which we can add back later), it will look like this:

10000+100x+100y+xy. In other words, statement (2) gives us exactly the variables we need to solve the total percentage increase.

This statement is sufficient.