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

It is currently 21 Sep 2018, 22:55

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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
Intern
User avatar
B
Joined: 31 Dec 2017
Posts: 19
Concentration: Finance
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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 = \(\frac{1}{5}\).
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
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

New post 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

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/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Intern
avatar
B
Joined: 16 Oct 2017
Posts: 38
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
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

New post 15 Feb 2018, 12:24
1
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

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/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Director
Director
User avatar
P
Joined: 09 Mar 2016
Posts: 876
Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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:

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

Answer: D.


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 :)
_________________

In English I speak with a dictionary, and with people I am shy.

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1978
Premium Member CAT Tests
Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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.)
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Manager
Manager
avatar
S
Joined: 29 Sep 2017
Posts: 113
Location: United States
Concentration: Strategy, Leadership
GMAT 1: 720 Q49 V39
GPA: 3.3
WE: Consulting (Consulting)
GMAT ToolKit User Reviews Badge
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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!

Director
Director
User avatar
P
Joined: 09 Mar 2016
Posts: 876
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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 :)
_________________

In English I speak with a dictionary, and with people I am shy.

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1978
Premium Member CAT Tests
Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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? :lol: :lol: :lol:
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 :thumbup: :thumbup:

QUESTION asks
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. :-)
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Intern
Intern
avatar
B
Joined: 17 Oct 2016
Posts: 1
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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
Answer D=1/5
Intern
Intern
avatar
B
Joined: 03 Aug 2017
Posts: 3
GMAT ToolKit User
Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

Show Tags

New post 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 :)
Re: Alice’s take-home pay last year was the same each month, and &nbs [#permalink] 16 Sep 2018, 11:12

Go to page   Previous    1   2   [ 32 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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.