This ratio question is scary!

GRE Quant Problem Solving
1

Two classes A and B have students in the ratio 15: 42.

Quantity A = The number of students from class B must be shifted to class A so that class A will have double the students than that in class B ?

Quantity B = 23

2

So… do you want help?

3

yes sir

4

I am very much confused between option C and option D

5

Okay, can you show how u got to C or D?

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6

yes surely,

if the number of students shifting from class b to class a is let’s say “x” then the new ratio would be 2:1 according to question right.

so we can write

15+x/42-x = 2/1

and that would give the value of x
which would be 23

then, we can find to what factor the ratio increased

15y+23=2(42y-23) #as it is double
then it would result in 1

so we know that total number of students shifted is 23. So answer is C

but here is my question we can also do like 15y and 42y and still make a shift such that it ratio become double the class B in class A . sooo you know it can be 46 students …
so it is not possible to get answer without knowing what factor it is getting increased right
so answer could be D…

omg i just realised how terribly i have answered…

7

Yeah, i think you’ve solved it.

How i would do it is basically:

2 = \frac AB = \frac{5y + x}{14y - x} \implies \frac{23y}{3} = x

This means that integer solutions for x occur exactly when y = 3k, for k in \mathbb{N}. This goes on to imply that x can be any positive multiple of 23.

To address your actual question, you considered a specific value of y (namely y = 3 which occurs when k = 1) to land at answer C, but any positive integer you select for k would give valid values of y and thus x.

P.S. our variables mean the same thing, so as to cause less confusion to you

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8

so answer is D?

9

Yes, for the reason I mentioned.

To restate, x can be any positive multiple of 23.

For example, if we suppose x = 46 (and thus consequently y = 6), then you could have something like:

\frac{30 + 46}{84 - 46} = 2, which works out well according to the constraints in the question

In case, you don’t get what those numbers mean then:

  • 30 = number students in Class A

  • 84 = number of students in class B

  • 46 = number of shifted students

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10

thanks a lot good sir :))

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