By what percent did the infant mortality rate in Country X decrease

Question

By what percent did the infant mortality rate in Country X decrease from 1972 to 1976?

(1) On average, the infant mortality rate in Country X decreased by 10% per year from 1972 to 1976.
(2) On average, the infant mortality rate in Country X decreased by 8% per year from 1970 to 1980.

What is the difference between the two statement.

one statement is sufficient the other not , why So?

please explain.

IanStewart · Answer

It's not clear what the phrase "on average" means in either Statement, so there's no way to answer the question. What is being averaged? Is it the percentage point decreases each year? Or is it the overall percent decrease divided by 4? Those are very different things. If it's the former, the answer is E (because maybe it dropped 40% one year, and 0% the other three years, for an overall decrease of 40% ,or maybe it dropped 10% each year, and then because of compounding, the overall decrease would have been less than 40%). If it's the latter, the answer is clearly A.

MKpatel · Answer

Statement 1: On average, the infant mortality rate in Country X decreased by 10% per year from 1972 to 1976.
Since we know the average percent decrease each year, we can calculate the total percent decrease for the entire period.
SUFFICIENT.

Statement 2: On average, the infant mortality rate in Country X decreased by 8% per year from 1970 to 1980.
Here, the SUM of the percent decreases for the entire 10 years = number*average = 10*8 = 80.
It's possible that the average percent decrease each year from 1972 to 1976 was 20%, while the average percent decrease for the remaining 6 years was 0%, since (4*20) + (6*0) = 80.
It's possible that the average percent decrease each of the 10 years -- including from 1972 to 1976 -- was 8%.
Since different percent decreases are possible, INSUFFICIENT.

JeffTargetTestPrep · Answer

We need to answer the question:

percent decrease from 1972 to 1976 = ?

Statement One Alone:

=> On average, the infant mortality rate in Country X decreased by 10% per year from 1972 to 1976.

In economics, the usual way to interpret an average of percent changes is to think in terms of factors.

“10% decrease” corresponds to a factor of 0.9, and the number of elapsed years is 4, so we have:

rate_1976 = rate_1972 × 0.9 × 0.9 × 0.9 × 0.9 = (rate_1972)(0.9)^4

We could determine the total percent change by evaluating the factor (0.9)^4.

Statement one is sufficient. Eliminate answer choices B, C, and E.

(Note: (0.9)^4 = 0.6561, a factor that corresponds to a (1 – 0.6561)×100 = 34.39 percent decrease. Of course, on the GMAT, we don’t need to determine the exact value of (0.9)^4.)

Statement Two Alone:

=> On average, the infant mortality rate in Country X decreased by 8% per year from 1970 to 1980.

Using the same logic as above, we could determine the total percent decrease from 1970 to 1980. However, we can’t infer anything about the total percent decrease during the subperiod 1972 to 1976.

Statement two is not sufficient.

Answer: A

anirchat · Answer

The correct intuition here is that in case of Statement 2), we are given the average decrease per year. However, we are asked to calculate the abosolute decrease from 1972 to 1976. Hence, it is ambiguous. So B cannot help us in determining the answer.

So A) is the right answer.

So A) is the right answer.

By what percent did the infant mortality rate in Country X decrease

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