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Alice’s take-home pay last year was the same each month, and

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Alice’s take-home pay last year was the same each month, and [#permalink] New post 26 Mar 2010, 16:21
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Mar 2012, 00:53, edited 1 time in total.
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Re: please help me set up the equation for this problem [#permalink] New post 26 Mar 2010, 16:39
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changhiskhan 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 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

Thanks,



Let Alice's monthly take-home pay be p and her monthly savings be s. Total savings will be 12s and we know that this is 3 times the amount she spends in month which is: p-s. So we have:

12s=3(p-s) --> s=p\frac{1}{5}

Answer: D.
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Re: please help me set up the equation for this problem [#permalink] New post 27 Mar 2010, 03:17
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changhiskhan 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 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
Thanks,

x - monthly take home
y - monthly save
x-y - monthly expenditure
given, 12y = 3(x-y) => x = 5y
to calculate, y/x = 1/5 hence D
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Re: PS-gprep [#permalink] New post 04 Jul 2010, 12:28
ramana wrote:
I know i am terribly missing something, please elaborate

OA soon


Let's call the fraction of pay PER MONTH that Alice saved S, and the fraction of pay that she did not save N.
Therefore:
(% of pay saved) + (% of pay spent) = 100%
S + N = 1

The second sentence in the question states that Alice's total yearly savings is equal to three times the amount she would NOT save (a.k.a. the spending) in one month.
Therefore:
(yearly savings) = (3 * monthly spending)
(12 * monthly saving) = (3 * monthly spending)
12S = 3N
4S = N

Now plug this into the top equation to find a value for S:
4S = N
S + N = 1
S + (4S) = 1
5S = 1
S = 1/5

Therefore, the answer is D.


I'd be willing to bet that you didn't read carefully enough and you thought the second sentence in the question said, " The total amount of money at the end of the year that she had saved was 3 times the portion that she had spent." This is what I thought during my first read-through -- and I spent about 15 seconds working the problem incorrectly!
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Re: PS-gprep [#permalink] New post 05 Jul 2010, 01:11
YourDreamTheater wrote:
I'd be willing to bet that you didn't read carefully enough and you thought the second sentence in the question said, " The total amount of money at the end of the year that she had saved was 3 times the portion that she had spent." This is what I thought during my first read-through -- and I spent about 15 seconds working the problem incorrectly!


Damn, i got this wrong! :(
you are absolutely right.! I got a completely diffrent fraction cos of my carelessness!
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Re: please help me set up the equation for this problem [#permalink] New post 10 Feb 2011, 09:12
Alice's pay each month = $x
Alice's saving each month = $y
Alice did not save each month = $x -$y

Total Saving per year: 12y

12y = 3(x-y) ---1st

y/x = ?

4y=x-y
4=x/y-1
x/y=5

y/x=1/5

Ans: "D"
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Re: please help me set up the equation for this problem [#permalink] New post 18 Nov 2011, 05:51
Lets say that the total monthly revenue is R and she saved \frac{1}{x} of this revenue every month.
So based on the question:

12 (\frac{1}{x}) R = 3 (1- \frac{1}{x}) R

x=5

So she saved \frac{1}{5} of monthly revenue.
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Re: Proportion of Take home pay saved [#permalink] New post 18 Mar 2012, 21:04
Let her monthly take-home be x and her monthly savings be y.
Then 12y = 3(x-y)
=> y/x = 1/5

Option (D)
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Re: Proportion of Take home pay saved [#permalink] New post 18 Mar 2012, 22:25
GyanOne wrote:
Let her monthly take-home be x and her monthly savings be y.
Then 12y = 3(x-y)
=> y/x = 1/5

Option (D)


Thank you. I initially did the equations as
12y = 3 x 12 (x-y) so didn't get it right.
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Re: Proportion of Take home pay saved [#permalink] New post 18 Mar 2012, 22:58
D
12x=3(y-x)
=> x/y=1/5
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 27 Mar 2012, 17:30
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 07 Apr 2014, 10:57
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 03 Jul 2014, 17:36
changhiskhan 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 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


I had a different approach to this question and I still don't understand why it doesn't work this way. Because the way people on this thread used, didn't come to my mind at all.

So let x be the amount she earns each month. Then she earned total of 12x in a year.

so I know that from this amount 3x was spent and 9x was saved.

so 9x/12=3x/4 was her monthly save.

(3x/4)/x= 3/4

and there isn't even an answer like that. I must be getting something completely wrong but I can't seem to understand where exactly i'm going wrong.
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 04 Jul 2014, 02:02
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bytatia wrote:
changhiskhan 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 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


I had a different approach to this question and I still don't understand why it doesn't work this way. Because the way people on this thread used, didn't come to my mind at all.

So let x be the amount she earns each month. Then she earned total of 12x in a year.

so I know that from this amount 3x was spent and 9x was saved.

so 9x/12=3x/4 was her monthly save.

(3x/4)/x= 3/4

and there isn't even an answer like that. I must be getting something completely wrong but I can't seem to understand where exactly i'm going wrong.


The total amount of money that she saved in a year was 3 times the amount of the money she spent per month.
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 04 Jul 2014, 02:37
bytatia wrote:
changhiskhan 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 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


I had a different approach to this question and I still don't understand why it doesn't work this way. Because the way people on this thread used, didn't come to my mind at all.

So let x be the amount she earns each month. Then she earned total of 12x in a year.

so I know that from this amount 3x was spent and 9x was saved.

so 9x/12=3x/4 was her monthly save.

(3x/4)/x= 3/4

and there isn't even an answer like that. I must be getting something completely wrong but I can't seem to understand where exactly i'm going wrong.


The problem does not state that 1/4 th of the amount earned is spent OR 3/4 th of the amount earned in saved.

We have to take another variable to compute the savings amount & draw relation between Total saved & Not Saved

As always, Bunuel's method is the best to get along :)
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Alice's take home pay [#permalink] New post 27 Jul 2014, 10:18
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 that portion of the 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


Please explain the same. Answer is D 1/5
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Alice's take home pay [#permalink] New post 27 Jul 2014, 10:55
msharmita 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 that she saved at the end of the year was 3 times the amount of that portion of the 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


Please explain the same. Answer is D 1/5



Here lies the explanation -

Suppose fraction of her take home pay she did save each month = \frac{x}{y}
then fraction she did NOT save each month will be 1- \frac{x}{y} = \frac{(y-x)}{y}

Now we are given that
whatever she saved in last year (in 12 months) =\frac{12*x}{Y} = 3 \frac{(y-x)}{y}
=> 12 x = 3 (y-x)
=> 15 x = 3 y
=>\frac{x}{y}= \frac{3}{15} = \frac{1}{5} = ANS D

Hope it helps :-)
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Re: Alice's take home pay [#permalink] New post 27 Jul 2014, 10:58
Dear msharmita,

Good question, however; I request that you put this question in proper format as provided by gmatclub forum.
(gmatclub provides some nice template along-with in-built timer :) )
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post 27 Jul 2014, 13:35
Expert's post
msharmita 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 that she saved at the end of the year was 3 times the amount of that portion of the 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


Please explain the same. Answer is D 1/5


Merging topics. Please refer to the discussion above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 2, and 3. Thank you.


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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Alice’s take-home pay last year was the same each month, and   [#permalink] 27 Jul 2014, 13:35
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