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

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albany09
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Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   06 Oct 2008, 09:00
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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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B
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zonk
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Re: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   06 Oct 2008, 10:35
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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: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   06 Oct 2008, 11:20
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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.
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B
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Re: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   12 Feb 2020, 05:22
By looking at the answer choices we can solve this problem by working backwards.

If we choose B) 750 as a starting point we find that:

1/3 have 5-star ratings is = 250
2/3 have other ratings is = 500
2/5 of remaining have 5 stars = 500 * 2/5 = 200
Remaining is 300 which matches with the remaining 300 that have 3-star ratings.
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Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   14 Feb 2020, 14:24
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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


Solution:

We can create the equation:

T = T/3 + 2/5(2T/3) + 300

T = T/3 + 4T/15 + 300

T = 5T/15 + 4T/15 + 300

T = 9T/15 + 300

15T/15 - 9T/15 = 300

6T/15 = 300

2T/5 = 300

2T = 1500

T = 750

Alternate Solution:

We are given that 1 - 1/3 = 2/3 of the mutual funds are not 5-star, and, of these non-5 star funds, 1 - 2/5 = 3/5 of them are 3-star funds. Since there are 300 3-star funds, there are 300/(3/5) = 500 non-5-star funds. Thus, the total number of mutual funds is 500/(2/3) = 750.

Answer: B
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Re: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink] New post   25 Jan 2022, 09:13
Hello from the GMAT Club BumpBot!

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Re: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and [#permalink]
25 Jan 2022, 09:13
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