A total of 774 doctorates in mathematics were granted to United States

Question

A total of 774 doctorates in mathematics were granted to United States citizens by American universities in the 1972-1973 school year, and W of these doctorates were granted to women. The total of such doctorates in the 1986-1987 school year was 362, and w of these were granted to women. If the number of doctorates in mathematics granted to female citizens of the United States by American universities decreased from the 1972-1973 school year to the 1986-1987 school year, was the decrease less than 10 percent?

(1) 1/10 < W/774 < 1/9
(2) W = w + 5

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Official Answer

C

(1) 1/10 < W/774 < 1/9
(2) W = w + 5

uday1409 · Answer

No info on w so insufficient
2. Many such combinations possible with some greater than 10% or less than 10%
Insufficient

1+2>>> From 1, we have W between 77.4 and 85(excluded). So W can take 78 79 ...84 values...for each W there is w less than 5.
So we have the boundaries for decrease in percentage as 5/78 and 5/84. Which are less than 10%.
So ans is C

ramlala · Answer

Hi  chetan2u   Bunuel

Decrease in % does not mean  \frac{W - w }{ 774} * 100  ?

Can we not find it from Statement 2 ?

chetan2u · Answer

We know that the doctorates granted went down from 1972-1973 school year to the 1986-1987 school year. In terms of variable, it went down from W to w. We are asked about the decrease. => \frac{W-w}{W}*100 . The numbers 774 and 362 are distractions which have no role in the question. So statement 2 is not sufficient. (1) \frac{1}{10} < \frac{W}{774} < \frac{1}{9} \frac{1}{10}=\frac{77.4}{774} < \frac{W}{774} < \frac{1}{9}=\frac{86}{774} So W can be any value from 78 to 85, both inclusive. Nothing about w. Insufficient (2) W = w + 5 W-w=5, but we require value of W in \frac{W-w}{W}*100 . Is \frac{W-w}{W}*100<10.......\frac{5}{W}<\frac{1}{10}.......W>50 . So using statement II, we will have answer yes if W>50, otherwise No. But we do not know the exact value of W. Insufficient Combined From statement II, the answer will be yes if W>50, and statement I gives range of W greater than 50. So answer is always yes. Sufficient C

anirchat · Answer

I think this is non-standard.

Decrease  in the number of doctorates in mathematics granted to female citizens means :
{((W/100)*774 -(w/100)*360)/774}*100

Why does the question exoect me to consider  Decrease  as {(W-w)/W}*100

For the second thing to be correct, it should be mentioned clearly as Decrease in %.

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A total of 774 doctorates in mathematics were granted to United States

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