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# To Ell a larger concert hall, a madrigal singing group consisting of

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Math Expert
Joined: 02 Sep 2009
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To Ell a larger concert hall, a madrigal singing group consisting of  [#permalink]

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05 Feb 2019, 02:15
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Difficulty:

65% (hard)

Question Stats:

44% (01:54) correct 56% (01:39) wrong based on 32 sessions

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To Ell a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio, needs 40 singers. What is the least number of basses the group will need?

A. 8
B. 9
C. 10
D. 11
E. 12

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Re: To Ell a larger concert hall, a madrigal singing group consisting of  [#permalink]

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05 Feb 2019, 04:09
1
IMO A

In the given multipart ratio, the proportion of Basses among 40 singers is - $$\frac{3}{15} * 40 = 8$$
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Re: To Ell a larger concert hall, a madrigal singing group consisting of  [#permalink]

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05 Feb 2019, 22:55
GMATMBA5 wrote:
IMO A

In the given multipart ratio, the proportion of Basses among 40 singers is - $$\frac{3}{15} * 40 = 8$$

I didn't pay attention to the count of altos and sopranos when arriving to the count of basses as 8.
I guess the question stem should include "AT LEAST" 40 singers....
And with that we can arrive on 9 basses, 21 altos and 15 sopranos.

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Re: To Ell a larger concert hall, a madrigal singing group consisting of  [#permalink]

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06 Feb 2019, 00:33
Bunuel wrote:
To Ell a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio, needs 40 singers. What is the least number of basses the group will need?

A. 8
B. 9
C. 10
D. 11
E. 12

For the madrigal singing group in the ratio to have a ratio of 5:7:3(S:A:B),
for every 3x basses, there are 12x sopranos and altos. Since we need the
least number of basses

15x(3x + 12x) > 40 or x > 2.66. The minimum value of x is 3

Therefore, the least number of basses the group will need is 3x or 9(Option B)
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Re: To Ell a larger concert hall, a madrigal singing group consisting of  [#permalink]

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11 Feb 2019, 02:54
Bunuel wrote:
To Ell a larger concert hall, a madrigal singing group consisting of sopranos, altos, and basses, in a 5:7:3 ratio, needs 40 singers. What is the least number of basses the group will need?

A. 8
B. 9
C. 10
D. 11
E. 12

At least 40 means it can be greater but not less than 40

S:A:B
5:7:3
Multiply the ratio by 3
15+21+9 = 45

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Re: To Ell a larger concert hall, a madrigal singing group consisting of   [#permalink] 11 Feb 2019, 02:54
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