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Over the past year, did the number of male students in the school incr

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Over the past year, did the number of male students in the school incr  [#permalink]

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New post 07 Jan 2018, 23:16
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Over the past year, did the number of male students in the school increase?

(1) Over the past year, the ratio of number of male students to the total number of students increased.
(2) Over the past year, the total number of female students increased.

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Re: Over the past year, did the number of male students in the school incr  [#permalink]

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New post 08 Jan 2018, 02:10
Bunuel wrote:
Over the past year, did the number of male students in the school increase?

(1) Over the past year, the ratio of number of male students to the total number of students increased.
(2) Over the past year, the total number of female students increased.


Answer C.

Quick logical solution: ratios describe equations in which there are three factors: two quantities and the ration between them. This means that to find what happened to one quantity (which is what we are asked) we need the other two factors. Each statement gives us one of them - we need both. Combined.

Precise solution: the question describes an equation:
male students - m, female students = f, ratio between male and female students = r
m = f X r
(1) m = f X r+ - but without knowing what happened to f, we don't know what happened to m
(2) m = f+ X r - but without knowing what happened to r, we don't know what happened to m
Combined: m = f+ X r+ > m+ Sufficient!

Alternative solution, using easy numbers:
let's say there were two females and two males to begin with.
(1) let's say the ratio of \frac{male}{female} grew from \frac{1}{1} to \frac{2}{1}. If the number of females stayed the same (2), that means the number of males must have grown to 4. BUT, if the number of females decreased to 1, then the number of males stayed the same (2 = \frac{2}{1}). Insufficient!
(2) Let's say the number of female students grew to 4. If the ratio stayed the same, the number of males must also have grown (1 = \frac{4}{4}). But if the ratio changed, the males could have stayed the same (\frac{1}{2} - \frac{2}{4}). Insufficient!
Combined: females grew to 4 and ratio grew to 2: 2 = \frac{m}{4} > m = 8 - number of males definitely grew - sufficient!
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