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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Wed Mar 14, 2018 1:47 pm

From a group of boys and girls, 15 girls leave. There are then let two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was?

A. 29
B. 40
C. 43
D. 48
E. None of these

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Mar 14, 2018 1:47 pm

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Mar 14, 2018 9:26 pm

swerve wrote:From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was?

A. 29
B. 40
C. 43
D. 48
E. None of these

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Say there were x girls.

After the 15 gilrs left, the number of girls left = (x - 15)
=> the number of boys now = 2(x - 15) = 2x - 30; it is given that there are then left two boys for each girl

After 45 boys left, the number of boys left = 2x - 30 - 45 = 2x - 75
=> the number of girls now = 5(2x - 75) = 10x - 375; it is given that there are then 5 girls for each boy

10x - 375 must be equal to x - 15

Thus, 10x - 375 = x - 15

=> x = 40

The correct answer: B

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Mar 19, 2018 5:48 am

swerve wrote:From a group of boys and girls, 15 girls leave. There are then let two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was?

A. 29
B. 40
C. 43
D. 48
E. None of these

We can let b = number of boys and g = number of girls originally in the group. Thus, we have:

b/(g - 15) = 2/1

and

(b - 45)/(g - 15) = 1/5

Simplifying the first equation, we have:

b = 2(g - 15)

b = 2g - 30

Substituting this into the second equation, we have:

(2g - 30 - 45)/(g - 15) = 1/5

5(2g - 75) = g - 15

10g - 375 = g - 15

9g = 360

g = 40

Answer: B

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