GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jun 2019, 08:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 31 Dec 2017
Posts: 28
Concentration: Finance
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

09 Feb 2018, 18:07
1
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

pay per month = $$x$$
pay last year = $$12x$$

savings per month = $$\frac{1}{y}(x) = \frac{x}{y}$$
savings last year = $$\frac{12x}{y}$$

spending each month = $$x - \frac{x}{y} = \frac{(xy-x)}{y}$$
spending last year = $$\frac{12(xy-x)}{y}$$

$$\frac{12x}{y} = \frac{3[xy-x]}{y}$$
$$\frac{4x}{y} = \frac{xy-x}{y}$$
$$4x = xy-x$$
$$5x = xy$$
$$y = 5$$.

Fraction = $$\frac{1}{5}$$.
Intern
Joined: 16 Oct 2017
Posts: 37
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

14 Feb 2018, 19:08
EMPOWERgmatRichC wrote:
Hi All,

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

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Can this be solved using smart numbers? For example, by using $120 for take-home pay to represent 12 months? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14378 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 14 Feb 2018, 21:09 Hi OCDianaOC, Yes, you could solve this question by TESTing VALUES. To use that approach efficiently though, you wouldn't start with Alice's take-home pay each month - you'd actually have to start with the information in the second sentence: "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." By TESTing VALUES that fit this information, you can then 'work backwards' and determine her take-home pay each month (and then answer the question). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Intern
Joined: 16 Oct 2017
Posts: 37
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

14 Feb 2018, 23:19
EMPOWERgmatRichC wrote:
Hi OCDianaOC,

Yes, you could solve this question by TESTing VALUES. To use that approach efficiently though, you wouldn't start with Alice's take-home pay each month - you'd actually have to start with the information in the second sentence:

"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."

By TESTing VALUES that fit this information, you can then 'work backwards' and determine her take-home pay each month (and then answer the question).

GMAT assassins aren't born, they're made,
Rich

Thanks Rich, but I'm not getting the correct answer by testing values.

I chose that she saved $10/month and had$120 by the end of the year. She did NOT save $40 (since$120 is 3 times bigger than $40). Total take-home pay is$1,200/year.

My answer: I got 10/100 then reduced to 1/10. Wrong answer!

Help!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14378
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

15 Feb 2018, 12:24
2
Hi OCDianaOC,

The numbers you've chosen to TEST are perfect, but you made a small math mistake:

IF... $10 was saved each month and$40 was NOT saved each month, then the total for each month is $50 (not$100). Thus, the take-home pay for the year would be (12)($50) =$600.

Total saved for the year = (12)($10) =$120
Total take-home pay for the year = $600$120/$600 = 1/5 GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
VP
Joined: 09 Mar 2016
Posts: 1274
Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

15 May 2018, 04:22
Bunuel 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

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:

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

Hello Bunuel - founder of numerology hope you are well

my solution is quite unusual but is super duper quck

As per this sentence " Alice 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'

So total amount she saved was 60 and total amount she didnt save was 20

So now question is "what fraction of her take-home pay did she save each month?"

so i divide 60 by 12 (number of months ) 60/12 = 5

hence $$\frac{1}{5}$$ she saved each month. YAY

is my correct approach ?

thanks and have a good week

in case Bunuel doesn't reply I will tag you friends too generis niks18
Senior SC Moderator
Joined: 22 May 2016
Posts: 2936
Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

15 May 2018, 09:16
1
dave13 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

Hello Bunuel - founder of numerology hope you are well

my solution is quite unusual but is super duper quck

As per this sentence " Alice 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'

So total amount she saved was 60 and total amount she didnt save was 20

So now question is "what fraction of her take-home pay did she save each month?"

so i divide 60 by 12 (number of months ) 60/12 = 5

hence $$\frac{1}{5}$$ she saved each month. YAY

is my correct approach ?

thanks and have a good week

in case Bunuel doesn't reply I will tag you friends too generis niks18

Hi dave13 , whether your approach is correct depends on whether
you did some mental math and did not write down the steps.

How did you calculate $$\frac{1}{5}$$?
How did you go from 5 to $$\frac{1}{5}$$?
(You have everything in place. You picked good numbers.
How and whether you manipulated those numbers, I cannot discern.)
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
Manager
Joined: 29 Sep 2017
Posts: 117
Location: United States
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

15 May 2018, 11:28
1
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

Notice that the 60 is a good number to change fractions to whole numbers; hence, each choice becomes:
A. 30
B. 20
C. 15
D. 12
E. 10

Simply plug and play: if her take home savings were $30, then she did not save$30. 12(30) = 360. Divide this by amount not saved ($30); hence, 12. We need this to be 3x, not 12x. Plugging in rest of numbers shows that D (12) fits. 12 (amount saved) * 12 (months in a year) = 144 (amount saved in year) 48 (amount not saved) * 3 (per stem) = 144. Both match; hence, D. _________________ If this helped, please give kudos! VP Joined: 09 Mar 2016 Posts: 1274 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 15 May 2018, 12:01 generis wrote: dave13 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 Hello Bunuel - founder of numerology hope you are well my solution is quite unusual but is super duper quck As per this sentence " Alice 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' So total amount she saved was 60 and total amount she didnt save was 20 So now question is "what fraction of her take-home pay did she save each month?" so i divide 60 by 12 (number of months ) 60/12 = 5 hence $$\frac{1}{5}$$ she saved each month. YAY is my correct approach ? thanks and have a good week in case Bunuel doesn't reply I will tag you friends too generis niks18 Hi dave13 , whether your approach is correct depends on whether you did some mental math and did not write down the steps. How did you calculate $$\frac{1}{5}$$? How did you go from 5 to $$\frac{1}{5}$$? (You have everything in place. You picked good numbers. How and whether you manipulated those numbers, I cannot discern.) Greetings generis i simply took number 60 because it is easy to work with (it can be divided by 2, 3, 4, 5, 6, 10 and 12) very practical number so since her total amount saved for the whole year is 60 and we need to know how much she saved monthly i divided 60 by 12 = 5 i added 1 in numeror to match it to answer choice i decorated my answer by adding a personal touch optionally $$\frac{12}{60}$$= $$\frac{1}{5}$$ have a lovely jovely day Senior SC Moderator Joined: 22 May 2016 Posts: 2936 Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 15 May 2018, 13:04 1 1 1 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 dave13 wrote: generis wrote: dave13 wrote: Hello Bunuel - founder of numerology hope you are well my solution is quite unusual but is super duper quck As per this sentence " Alice 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' So total amount she saved was 60 and total amount she didnt save was 20 So now question is "what fraction of her take-home pay did she save each month?" so i divide 60 by 12 (number of months ) 60/12 = 5 hence $$\frac{1}{5}$$ she saved each month. YAY is my correct approach ? thanks and have a good week in case Bunuel doesn't reply I will tag you friends too generis niks18 Hi dave13 , whether your approach is correct depends on whether you did some mental math and did not write down the steps. How did you calculate $$\frac{1}{5}$$? How did you go from 5 to $$\frac{1}{5}$$? (You have everything in place. You picked good numbers. How and whether you manipulated those numbers, I cannot discern.) Greetings generis i simply took number 60 because it is easy to work with (it can be divided by 2, 3, 4, 5, 6, 10 and 12) very practical number so since her total amount saved for the whole year is 60 and we need to know how much she saved monthly i divided 60 by 12 = 5 i added 1 in numeror to match it to answer choice i decorated my answer by adding a personal touch optionally $$\frac{12}{60}$$= $$\frac{1}{5}$$ have a lovely jovely day Your personal touch? OMG. What, did you try some numerology, too? I am SO hoping (and so NOT hoping) he sees that one. You are ABSOLUTELY correct about the number 60 (and 120, BTW). Now, let's finish this . . .You wrote: Quote: we need to know how much she saved monthly i divided 60 by 12 = 5 True. Good instincts. We also need to know how much she EARNED monthly Quote: So total amount she saved was 60 andtotal [MONTHLY] amount she didnt save was 20 Saved$60 in one YEAR
$60 is three times$20, which is the amount she did NOT save EACH MONTH
Per month SAVED?
Per month NOT SAVED?

This step is correct: $$$\frac{60}{12}$$ =$5 per month SAVED

Quote:
what fraction of her take-home pay did she save each month?

1) Find take home pay per month = (Dollars saved each month) + (Dollars NOT saved each month)

Take home pay per month (with the awesome numbers you picked) is:
$5 (saved) +$20 (not saved) = $25 per month 2) Now, what fraction of that monthly pay did she save? • saved each month:$5
• earned each month: $25 $$\frac{SavedAmt}{MonthlyAmt}=\frac{Part}{Whole}=\frac{5}{25}=\frac{1}{5}$$ You were very close! It is a good thing to look for simple shortcuts. Just make sure you read the question really carefully. (This question's language is not easy. I would bet that if you had read carefully, you would have found the answer.) You chose good numbers. Does this make sense? Thanks for making me laugh. _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver Intern Joined: 17 Oct 2016 Posts: 1 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 10 Jun 2018, 16:07 1 I tried to solve this testing the answers: I assumed her take home was$100

Testing 1/5th
Saving/month is 20; Saving/year is 240 (20*12)
Money not saved/Month is 80
80 is 1/3rd of 240
Intern
Joined: 03 Aug 2017
Posts: 11
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

16 Sep 2018, 11:12
In this problem we know that every payment across the year is the same, lets call those payments P.
Given this we know that we received at the end of the year 12P (p+p+p+p+p+....) 12 payments

Then we have 12P.

Ok, we also know that we save the same amount of money each month, lets call this S.
Given this we know that we save at the end of the year 12S (s+s+s+s+s+....) 12 "savings"

Then we have 12S.

Also the problem tell us that "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"

Before this we know that if she receives P every month, and she saves S, then the portion that she didn't saved was P-S.
So, lets translate this:

The total amount of money that she had saved the end of the year (12S) was (=) 3 times the amount of that portion of her monthly take-home pay that she did NOT save (3*(P-S))

Translation:

---> 12S=3(P-S)
so...
---> 4S = P-S
---> 5S = P
---> S/P = 1/5 (Answer)

S/P is the fraction of her monthly payment that she saved
Intern
Joined: 15 Nov 2018
Posts: 3
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

23 Dec 2018, 01:50
Let the total amount of money saved in a year = 900 (Money saved in a month = 900/12 =75)
and total amount of money spent in a year be = 300
Therefore, total amount of money saved in a year = 1200(Money saved in a month = 1200/12 = 100)

Therefore fraction of money saved in a month = 75/100 = 1/5
Intern
Joined: 07 Dec 2017
Posts: 4
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

15 May 2019, 09:10
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.

Amount Saved per month= 1/X
Not Saved per month = (1 - 1/X)

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.

12* 1/X = 3*(1-1/X)
12*1/X = 3 * [(X-1)/X] /*X
12=3(X-1)
4=X-1
5=X

Amount Saved per month= 1/X =1/5
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1360
Location: India
WE: Engineering (Other)
Alice’s take-home pay last year was the same each month, and  [#permalink]

### Show Tags

23 May 2019, 03:32

Quote:
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?

Quote:
Let monthly take home be 100 and the fraction she saves be x.

May I know how your genius mind came up with figure of 100 (was it because of highlighted text?,
still we choose 100 as base figure in %tage problems not in fractions)

Quote:
12*100*x = 3*100*(1-x)

Should not above expression be:

12*x = 3*(100-x)

Bunuel chetan2u we choose p and s as separate variables in the first post since there is no co-relation
between two as evident from first sentence of the problem. Am I correct in my understanding?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Alice’s take-home pay last year was the same each month, and   [#permalink] 23 May 2019, 03:32

Go to page   Previous    1   2   [ 35 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne