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A total of 774 doctorates in mathematics were granted to

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Director
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A total of 774 doctorates in mathematics were granted to [#permalink]

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New post 17 Aug 2008, 08:19
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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

Kudos [?]: 132 [0], given: 7

Intern
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Kudos [?]: 6 [0], given: 0

Re: tricky DS -- relative % decrease [#permalink]

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New post 17 Aug 2008, 09:47
7273: 774, W = Women
8687: 362, w = women

W/774 > w/362, less than 10%?

1. 1/10 < W/774 < 1/9
- Indicates W must be in between 78 and 86, but says nothing about w, insufficient.

2. W = w + 5
- Not sufficient as a very low value of W would make it exceed 10% while a high value of W would make it less than 10%.

Examples: 1 - 20/25 = 20%, 1 - 200/205 = 2.4%

- Combine both 1 & 2.
W must be in between 78 and 86, so w must be between 73 to 81

1 - 73/78 = 6.42%
1 - 81/86 = 5.81%

Within the range of 5.81% to 6.42%, so less than 10% decrease. (C)

Kudos [?]: 6 [0], given: 0

Senior Manager
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Re: tricky DS -- relative % decrease [#permalink]

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New post 18 Aug 2008, 08:25
(1) not sufficient. Not info is given on w.

(2)
W = w + 5
% decrease = [(W - w)/W]*100% = 500%/(w+5)
Not sufficient

(1) + (2)
(1/10) < (W/774) < (1/9)
77.4 < W < 86
because W is integer
78<= W <= 85
73<= w <= 80
When W = 78, w = 73
% decrease = 500%/(73+5) = 6.x% < 10%
When W = 85, w = 80
% decrease = 500%/(80+5) = 5.x% < 10%
=====> sufficient

Ans is C

Kudos [?]: 67 [0], given: 0

Re: tricky DS -- relative % decrease   [#permalink] 18 Aug 2008, 08:25
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A total of 774 doctorates in mathematics were granted to

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