Population Growth — GMAT Question of the Day
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September 30, 2021Population Growth — GMAT Question of the Day
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.
The correct answer is B.
