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All the 585 students of a school are divided into three different grou

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Bunuel
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All the 585 students of a school are divided into three different grou [#permalink] New post   19 Jun 2022, 22:45
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All the 585 students of a school are divided into three different groups such that the half the number of students in first group, one-third the number of students in second group and one-fourth the number of students in third group are equal. Find the number of students in each group.

A. 130, 195, 260
B. 260, 195, 130
C. 270, 130, 135
D. 135, 180, 270
E. None of these




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Re: All the 585 students of a school are divided into three different grou [#permalink] New post   20 Jun 2022, 05:28
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Let A, B, C be the number of students for the group 1, 2, 3, respectively. We have
A/2 = B/3 =C/4
A +B + C = 585

We can solve for A, and it is not too complicated.

But we can also observe answers by first checking C=2A
Only (A)(D) are possible choices. But 270 can not be divided by 4.
Double check (A) to confirm it satisfies the requirement.

So the answer is (A).
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Re: All the 585 students of a school are divided into three different grou [#permalink] New post   20 Jun 2022, 21:52
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Bunuel wrote:
All the 585 students of a school are divided into three different groups such that the half the number of students in first group, one-third the number of students in second group and one-fourth the number of students in third group are equal. Find the number of students in each group.

A. 130, 195, 260
B. 260, 195, 130
C. 270, 130, 135
D. 135, 180, 270
E. None of these


\(a + b + c = 585\) - (1)
\(a/2 = b/3 = c/4\) - (2)

From (2), \(c = 2a\)
Only A & D satisfy \(c = 2a\). Eliminate B & C.

From (2), c should be divisible by 4. Since 270 is not divisible by 4, eliminate D.

Verify Option A.

The answer is A.
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Re: All the 585 students of a school are divided into three different grou [#permalink] New post   20 Jun 2022, 23:14
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Let the students of groups first, second, and third be a, b, and c, respectively.
Now, by the given condition,

a/2 = b/3 = c/4

Or a : b : c = 2 : 3 : 4

Let a = 2x. Thus, b and c will be 3x and 4x, respectively.

Now since the total number of students is 585

2x + 3x + 4x = 585
9x = 585
x = 65

So, the students in groups first, second, and third are 130, 195, and 260, respectively.

And the correct option is A.
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Re: All the 585 students of a school are divided into three different grou [#permalink]
20 Jun 2022, 23:14
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