Doctorates

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Doctorates

by alexi_laiho » Wed Aug 06, 2008 6:31 am
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?

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

1. statement (A) alone is sufficient but statement (B) alone is not
2. statement (B) alone is sufficient but statement (A) alone is not
3. both (A) and (B) together are sufficient but none of them alone is sufficient
4. both statements are sufficient independently
5. both (A) and (B) together are not sufficient


Please provide ur answer with the explanation..thanks in advance
Source: — Data Sufficiency |

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by lunarpower » Thu Aug 07, 2008 12:24 am
this problem is fundamentally about inequalities - judging whether a particular number falls within a particular range - so you should consider EXTREME VALUES when appropriate.

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statement (1)
doesn't mention little 'w'
insufficient

statement (2)
consider extreme values.
one extreme: W = 5, w = 0. this is a 100% decrease, which is, obviously, greater than 10%.
other extreme: W = 367, w = 362 (can't go higher than this for 'w'). this is a decrease of 5/367, which is between 1% and 2%. (no need to calculate: 10% of 367 is 36.7, so this figure is way below 10%)
insufficient

(1) and (2) together
consider extreme values.
the lowest and highest possible values of W are 78 and 85 (because 1/10 < W/774 < 1/9 means 77.4 < W < 86, and it's "<", not "<").
if W = 78 and w = 73, then the decrease is 5 out of 78, which is less than 10% (note that 10% would be 7.8)
if W = 85 and w = 80, then the decrease is 5 out of 85, which is less than 10% (note that 10% would be 8.5)
so, less than 10% no matter what
sufficient

ans = c

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incidentally, the wording of this question is poor, especially by the unusually rigorous standards of the gmat. in particular, "such doctorates" is ambiguous; i had to read this question 3-4 times to make sense of it.
Ron has been teaching various standardized tests for 20 years.

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