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# Which school out of school A and school B has greater number of boys?

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Which school out of school A and school B has greater number of boys?  [#permalink]

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27 Jun 2018, 21:08
1
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:39) correct 44% (01:35) wrong based on 53 sessions

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Which school out of school A and school B has greater number of boys?

(1) Ratio of boys to girls in school A is less than ratio of boys to girls in school B.

(2) Girls in school A are more than girls in school B.
Intern
Joined: 21 May 2017
Posts: 42
Which school out of school A and school B has greater number of boys?  [#permalink]

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Updated on: 28 Jun 2018, 00:24
amanvermagmat wrote:
Which school out of school A and school B has greater number of boys?

(1) Ratio of boys to girls in school A is less than ratio of boys to girls in school B.

(2) Girls in school A are more than girls in school B.

Let boys in school A be b1 and girls in school A be g1.
Let boys in school B be b2 and girls in school B be g2.
We need to prove either b1>b2 or b1<b2.

Statement1
Let b1=4, g1=12, b2=2, g2=3
b1/g1 = 1/3
b2/g2 = 2/3
b1/g1 < b2/g2
We have b1 > b2

Now let's take b1=4, g1=12, b2=8, g2=12
b1/g1 = 1/3
b2/g2 = 2/3
b1/g1 < b2/g2
But, we have b1 < b2 this time.

So, statement 1 is insufficient.

Statement2
We know nothing about the number of boys. So, insufficient.

Statement1 & Statement2

We are given that b1/g1 < b2/g2 and g1>g2
b1/g1 < b2/g2
Let's multiply both sides by g1 (a positive integer)
b1 < b2 *g1/g2

And since g1>g2, we get g1/g2 > 1
Therefore,
b1 < b2*(something greater than 1)
Even now we cannot say which one is greater, b1 or b2.
Insufficient.

Edit: I misread Statement1, so updated.

Originally posted by ankitsaroha on 27 Jun 2018, 21:42.
Last edited by ankitsaroha on 28 Jun 2018, 00:24, edited 3 times in total.
Intern
Joined: 23 Jun 2018
Posts: 5
Which school out of school A and school B has greater number of boys?  [#permalink]

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28 Jun 2018, 00:03
The answer should be 'E' in my opinion

Statement 1 is insufficient as we don't know the exact number of students in each case
Statement 2 is insufficient as it doesn't mention any info about the number of boys.

Combining statement 1 and 2
b1/g1<b2/g2 and g1>g2

multiplying g1 on both sides,
b1<b2*g1/g2

here, g1/g2>1 (as g1>g2)

either b1<b2 or b1>b2 (as b2*1.something can be grater than b1 which will still hold the case to be true)
hence insufficient
Which school out of school A and school B has greater number of boys? &nbs [#permalink] 28 Jun 2018, 00:03
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