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GMATPrep - Take Home pay problem

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shannonalex: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jul 25, 2015 8:43 amFollowed by: 1 member

by shannonalex » Sat Jul 25, 2015 9:11 am

No idea how to address this problem

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Source: Beat The GMAT — Problem Solving | Sat Jul 25, 2015 9:11 am

shannonalex: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jul 25, 2015 8:43 amFollowed by: 1 member

by shannonalex » Sat Jul 25, 2015 9:23 am

I spent some more time searching and found the solution https://www.beatthegmat.com/word-problems-t270244.html

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Jul 25, 2015 9:43 am

Hi shannonalex,

We can solve this question with some algebra, but you have to be detailed with how you assign variables.

If...
X = the amount of money Alice EARNED per month
Y = the amount of money Alice SAVED per month
Y/X = the FRACTION of her paycheck she saved per month
then...
12Y = the amount of money Alice saved in ONE YEAR

Since the TOTAL amount saved = 3 times (what she DIDN'T save), we have this...
12Y = 3(X - Y)

Now, we can simplify:
12Y = 3X - 3Y
15Y = 3X
5Y = X
Y/X = 1/5

Final Answer: D

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Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jul 25, 2015 10:19 am

Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of her take-home pay that she didn't save. If all money she saved lasr year was from her take-home pay, what fraction of her pay did she save each month?

a)1/2
b)1/3
c)1/4
d)1/5
e)1/6

Let M = Alice's monthly take home pay
Let f = the fraction we'll use to calculate monthly savings
The means that fM = the amount of $ Alice saves each month.
And this means that her annual savings = 12fM

Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice does not save each month.

Now we're ready to write an equation.

The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M = [spoiler]1/5 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Sun Jul 26, 2015 4:03 am

Let Alice's take home pay per month be 100 and amount she saved per month be x => Amount she did not save per month is 100-x.

Set up equation with given facts:

Annual savings = 3 times annual expenditure

12x=3(100-x)

Solve for x => x=20

Thus, D.

Regards,

Pranay

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Jul 27, 2015 10:12 am

I solved the problem by plugging in some values and it worked well , here is my approach...

Salary not saved by alice is $10 per month

Salary not saved by alice after 1year is $120

Salary saved after 1 year is 3*$10 => $30

Total salary of alice = Salary not saved (After 1 year) + Salary saved by alice (After 1 year)

Total Salary = $150 (120 + 30)

Fraction of Take home pay saved each month is = Salary saved after 1 year / Total salary of alice after 1 year

Fraction of Take home pay saved each month is = 30/150 =>1/5

Abhishek

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 27, 2015 10:28 am

Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of her take-home pay that she didn't save. If all money she saved lasr year was from her take-home pay, what fraction of her pay did she save each month?

a)1/2
b)1/3
c)1/4
d)1/5
e)1/6

Let the amount saved each month = $1.
Total saved for the entire year = 12*1 = $12.
Since the total saved for the entire year -- $12 -- is 3 times the total not saved each month, the total not saved each month = 12/3 = $4.
Thus, the total monthly pay = (total saved each month) + (total not saved each month) = 1+4 = $5.
Resulting fraction:
(total monthly savings)/(total monthly pay) = 1/5.

The correct answer is D.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Wed Jul 29, 2015 12:08 am

statement is little ambiguous
Is it 3 times the monthly expenditure or annual expenditure

considering monthly expenditure

Monthly Take home Pay = P
Monthly Saving = S

Annual saving = 12 S
Annual Pay = 12 P

12S = 3 ( P - S)
15S = 3P
S = 1/5 P

Her saving is 1/5 of Pay.

Another ambiguous way of solving - considering 3 times yearly expenditure

Monthly Take home Pay = P
Monthly Saving = S

Annual saving = 12 S
Annual Pay = 12 P

12S = 3 ( 12P - 12S)
48 S = 36 P
S = 3/4 P

which is not given as option.

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