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Rate of decrease

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Rate of decrease

by sri_r » Mon Feb 25, 2013 3:50 am
Hi,
I have a doubt in the below question(from the GMAT Bible):

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.

The answer provided is A. The reasoning is if m is mortality rate in 1972, then for each year it will be 0.9*(previous year's rate).
so for 1976, it will be 0.9*0.9*0.9*0.9*m.
This is fine but here the value of m is not provided.

So shouldn't the answer be E?
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by Anurag@Gurome » Mon Feb 25, 2013 3:58 am
sri_r wrote: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.
Statement 1: Say, mortality rate in 1972 is m
Hence, mortality rate in 1976 is (0.9^4)*m

Hence, percentage decrease = [(m - (0.9^4)*m)/m]*100 = [1 - (0.9^4)]*100 ---> A definite value

Sufficient

Statement 2: This is not enough to determine the required percentage as we do not know what happened to the mortality rate in the particular period 1972 to 1976

Not sufficient

The correct answer is A.

sri_r wrote:...This is fine but here the value of m is not provided.
We do not need the value of m as the question did not asked for the mortality rate in 1976.
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by Deepthi Subbu » Thu Aug 08, 2013 2:23 am
Can we not assume the mortality rate for the year of 1970 as m, hence for 1972 it would be 0.92*0.92m and for 1976 0.92^6 m . So that wouldn't that be sufficient to calculate the percent decrease.
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by GMATGuruNY » Thu Aug 08, 2013 5:57 am
sri_r wrote: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.
This is a DS problem.
Do only as much calculating as necessary.

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.

The correct answer is A.
Last edited by GMATGuruNY on Thu Aug 08, 2013 6:11 am, edited 1 time in total.
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by Brent@GMATPrepNow » Thu Aug 08, 2013 6:09 am
Deepthi Subbu wrote:Can we not assume the mortality rate for the year of 1970 as m, hence for 1972 it would be 0.92*0.92m and for 1976 0.92^6 m . So that wouldn't that be sufficient to calculate the percent decrease.


For both statements, we are not told the individual percent decreases from year to year.
For statement 1, the individual percent decreases from year to year don't matter, because we're told that the average yearly decreases from 1972 to 1976, the exact same timeframe as in the target question.

In statement 2, because we're told that the average yearly decreases from 1970 to 1980. So, it could be the case that, between 1972 and 1976, there was a 1% decrease each year, then there were considerably bigger decreases during the other years (to create an overall average decrease of 8% for the 10 years). Or, it could be the case that, between 1972 and 1976, there was a 8% decrease each year. There's no way to be certain.

I hope that helps.

Cheers,
Brent
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