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 she 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 pay. If all the money that she saved last year was from her take-home pay, what fraction of her take-home did she save each month?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Please someone can help me explain this problem? Thanks!
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Alice's take-home pay last year was the same each month
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lunarpower
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you can pick a number for the monthly pay, because you don't ever find out what it is.
so just let the monthly pay be '1'.
let the monthly savings be 'S', which is both a fraction and an actual amount of money. (it's both because the monthly pay is '1', so the fraction is the same as the dollar amount -- this is the primary advantage of selecting a value of 1 as opposed to some other value)
then she has saved 12S at the end of the year.
each month, she didn't save (1 - S)
so
12S = 3(1 - S)
12S = 3 - 3S
15S = 3
S = 3/15 = 1/5
so just let the monthly pay be '1'.
let the monthly savings be 'S', which is both a fraction and an actual amount of money. (it's both because the monthly pay is '1', so the fraction is the same as the dollar amount -- this is the primary advantage of selecting a value of 1 as opposed to some other value)
then she has saved 12S at the end of the year.
each month, she didn't save (1 - S)
so
12S = 3(1 - S)
12S = 3 - 3S
15S = 3
S = 3/15 = 1/5
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Refer to the post: https://www.beatthegmat.com/alice-s-take ... tml#327957dtl wrote: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 she 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 pay. If all the money that she saved last year was from her take-home pay, what fraction of her take-home did she save each month?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Please someone can help me explain this problem? Thanks!
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We can plug in the answers, which represent the fraction saved each month.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 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. 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?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Answer choice C: 1/4
Let the total monthly pay = 4.
Amount saved each month = 1/4 * 4 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*3 = 9.
Since these last two values must be equal, too much money is being saved.
Eliminate A, B and C.
Answer choice D: 1/5
Let the total monthly pay = 5.
Amount saved each month = 1/5 * 5 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*4 = 12.
Success!
The correct answer is D.
Algebraically:
Let the fraction saved each month = x.
Amount saved for the whole year = 12x.
Fraction not saved each month = 1-x.
Since the amount saved for the whole year is equal to 3 times the fraction not saved each month, we get:
12x = 3(1-x)
12x = 3 - 3x
15x = 3
x = 3/15 = 1/5.
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Brent@GMATPrepNow
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Here's another algebraic approach.dtl wrote: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 she 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 pay. If all the money that she saved last year was from her take-home pay, what fraction of her take-home 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 doesn't 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]
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Scott@TargetTestPrep
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We are given 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.dtl wrote: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 she 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 pay. If all the money that she saved last year was from her take-home pay, what fraction of her take-home did she save each month?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
To start we can let S = the amount of money that Alice saved each month and N = the amount of money she did not save each month.
Since the 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 know that:
12S = 3N
4S = N
We need to determine what fraction of her take-home pay she saved each month. Setting this question up as an expression we have:
S/(S + N)= ?
Since 4S = N, we can substitute 4S in for for N in the expression S/(S + N).
S/(S + 4S) = S/5S = 1/5
Answer: D
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