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Bunuel
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A total of 774 doctorates in mathematics were granted to United States 15 Dec 2014, 09:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

65% (03:00) correct 35% (02:47) wrong based on 403 sessions

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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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C
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A total of 774 doctorates in mathematics were granted to United States 15 Dec 2014, 11:14
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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
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A total of 774 doctorates in mathematics were granted to United States 01 May 2021, 09:20
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Bunuel

Tough and Tricky questions: Word Problems.



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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Hi chetan2u Bunuel

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

Can we not find it from Statement 2 ?
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GMAT Focus 1: 735 Q90 V89 DI81
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A total of 774 doctorates in mathematics were granted to United States 01 May 2021, 09:45
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Bunuel

Tough and Tricky questions: Word Problems.



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


Kudos for a correct solution.

Hi chetan2u Bunuel

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

Can we not find it from Statement 2 ?
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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
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A total of 774 doctorates in mathematics were granted to United States 25 Mar 2025, 10:40
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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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