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The ratio of freshmen to sophomores to juniors in the room

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cbrelax
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The ratio of freshmen to sophomores to juniors in the room [#permalink] New post   Updated on: 05 Aug 2021, 00:22
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There are at least 10 freshmen in a room. The ratio of freshmen to sophomores to juniors in the room is 3 to 5 to 12. 40 percent of the freshman in the room are taking history, 60 percent of the sophomores in the room are taking history, and 36 percent of the total number of freshman, sophomores, and juniors in the room are taking history.

Quantity A
Quantity B
The percent of the juniors in the room taking history
30%


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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B

Originally posted by cbrelax on 04 Aug 2021, 22:10.
Last edited by Carcass on 05 Aug 2021, 00:22, edited 1 time in total.
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The ratio of freshmen to sophomores to juniors in the room [#permalink] New post   05 Aug 2021, 00:22
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cbrelax wrote:
There are at least 10 freshmen in a room. The ratio of freshmen to sophomores to juniors in the room is 3 to 5 to 12. 40 percent of the freshman in the room are taking history, 60 percent of the sophomores in the room are taking history, and 36 percent of the total number of freshman, sophomores, and juniors in the room are taking history.

Quantity A
Quantity B
The percent of the juniors in the room taking history
30%


F : S : J = 3x : 5x : 12x
Total students = 20x

Freshman in the room taking history = 0.4(3x) = 1.2x
Sophomores in the room taking history = 0.6(5x) = 3x
Juniors in the room taking history = a (let)
Total students in the room taking history = 0.36(20x) = 7.2x

Now, 7.2x = 1.2x + 3x + a
a = 3x

Col. A: \(\frac{3x}{12x}(100) = 25\)%
Col. B: \(30\)%

Hence, option B
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Re: The ratio of freshmen to sophomores to juniors in the room [#permalink] New post   05 Aug 2021, 00:22
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Please add always the answer choices to a QCQ questions

Good question
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Re: The ratio of freshmen to sophomores to juniors in the room [#permalink] New post   05 Aug 2021, 01:42
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Carcass wrote:
Please add always the answer choices to a QCQ questions

Good question


Oh I forget. Will keep in mind in future. Thanks.
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Re: The ratio of freshmen to sophomores to juniors in the room [#permalink] New post   06 Jun 2025, 13:58
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Re: The ratio of freshmen to sophomores to juniors in the room [#permalink]
06 Jun 2025, 13:58
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