home pay

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sat Jun 27, 2009 2:01 pm

Alice’s take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month.

oa [spoiler]1/5[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sat Jun 27, 2009 2:01 pm

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sat Jun 27, 2009 2:19 pm

For me it worked best to pick numbers b/c you are getting your answer in fraction form anyway.

Monthly pay = 100

portion saved monthly = x

so for the year she saved 12*x
which equals 3*(amount she did not save) = 3*(100-x)

so 12x = 3*(100-x)

4x = 100 - x

5x = 100

x = 20

so the fraction she saved every month would be 20/100 = 1/5

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sat Jun 27, 2009 2:33 pm

ssmiles08, good job. i was trying w/out picking numbers and it didn't work out..... let's see if someone else can give the answer only using variables...

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Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

by Morgoth » Sat Jun 27, 2009 3:03 pm

Let x be her monthly take home pay

Yearly = 12x

let y be the amount she save at the end of the year

therefore, y= 3*(x - y/12)

y = 3x/12 - 3y/12

y= x/4 - y/4 = (x-y)/4

4y = x - y

5y = x

y = x/5

fraction of her take home pay she saved each month = x/5 / x = x/5x = 1/5

Hope this helps.

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Sun Jun 28, 2009 6:46 am

Savings for the year = 3* did not save ( she saves the same amount each month)

Year = 12 months = 3*4

So did not save = 4* savings

Hence the answer is 1/5

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Sun Jun 28, 2009 10:10 pm

salary per month = 100
Savings = s
Expenses = 3

12s = 3e

s = 1/4 e

therefore 1/4 e + e = 100

e = 80
s = 1/4 e = 20

Fraction of saving = 20/100 = 1/5

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