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Of the mutual funds on a select list, 1/3 have 5-star

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Of the mutual funds on a select list, 1/3 have 5-star [#permalink] New post 06 Oct 2008, 09:00
Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?

A. 500
B. 750
C. 1,000
D. 1,200
E. 1,500
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Re: a math question [#permalink] New post 06 Oct 2008, 10:35
albany09 wrote:
Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?

A. 500
B. 750
C. 1,000
D. 1,200
E. 1,500


B

Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15
Fraction of 3-star funds = 1 - 9/15 = 6/15

(6/15)*Total = 300
Total = 750
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Re: a math question [#permalink] New post 06 Oct 2008, 11:20
albany09 wrote:
Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?

A. 500
B. 750
C. 1,000
D. 1,200
E. 1,500


Assume total X funds.

5-star = X/3
4-star = 2/5 * (X - X/3) = 2/5*(2X/3) = 4X/15
3-star = 300

5-star + 4-star + 3-star = total funds = X

X/3 + 4X/15 + 300 = X ---------- (1)
5X + 4X + 4500 = 15X ---------- (1) x 15
6X = 4500
X = 750

B is the answer.
Re: a math question   [#permalink] 06 Oct 2008, 11:20
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