From a group of boys and girls, 15 girls leave.

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 am; Location: India; Thanked: 5 times; Followed by:1 members

From a group of boys and girls, 15 girls leave.

by sachin_yadav » Mon Jun 17, 2013 11:18 am

From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning.

Answer is 40

What must be the right approach to solve this kind of question ? No other options are available in this question. It is an example from one of the conceptual books.

Thanks & Regards
Sachin

Never surrender

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Source: Beat The GMAT — Problem Solving | Mon Jun 17, 2013 11:18 am

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by GMATGuruNY » Mon Jun 17, 2013 1:45 pm

sachin_yadav wrote:From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning.

40 50 60 70 80

I've added answer choices, which the GMAT would provide.
We can plug in the answers for the original number of girls.

After 15 girls leave, the answer choices imply the following options for the remaining number of girls:
25, 35, 45, 55, 65

At this point there are 2 boys for each girl -- in other words, TWICE AS MANY boys as girls -- implying the following options for the number of boys:
50, 70, 90, 110, 130

Now 45 boys leave.
Subtracting 45 from each of our options for the number of boys, we get:
5, 25, 45, 65, 85

Resulting ratios of girls to boys:
25:5 = 5:1.
35:25 = 7:5.
45:45 = 1:1.
55:65 = 11:13.
65:85 = 13:17.

The required ratio of 5 girls for each boy is yielded by answer choice A.

The correct answer is A.

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fcabanski: Master | Next Rank: 500 Posts; Posts: 104; Joined: Fri Oct 07, 2011 10:23 pm; Thanked: 36 times; Followed by:4 members

by fcabanski » Mon Jun 17, 2013 3:55 pm

I would solve it by plugging in the answer choices.

You can also solve it with algebra.

b = boys
g = girls

15 girls leave. There are then left 2 boys for each girl.

1. b = 2*(g-15)

After this, 45 boys leave. There are then 5 girls for each boy.

2. 5*(b-45)= g-15

Substitute b (from 1) into 2.

5*(2g - 30 - 45) = g-15
10g -375 = g-15
9g = 360
g = 40

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 am; Location: India; Thanked: 5 times; Followed by:1 members