Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 15 Oct 2009
Posts: 11

Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
Updated on: 19 Mar 2012, 01:53
Question Stats:
62% (02:18) correct 38% (02:31) wrong based on 1782 sessions
HideShow timer Statistics
Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome pay did she save each month? A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by changhiskhan on 26 Mar 2010, 17:21.
Last edited by Bunuel on 19 Mar 2012, 01:53, edited 1 time in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: please help me set up the equation for this problem
[#permalink]
Show Tags
26 Mar 2010, 17:39
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome 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 takehome 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: \(ps\). So we have: \(12s=3(ps)\) > \(s=p\frac{1}{5}\) Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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 DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 22 Oct 2009
Posts: 235
GPA: 3.88

Re: PSgprep
[#permalink]
Show Tags
04 Jul 2010, 13:28
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 readthrough  and I spent about 15 seconds working the problem incorrectly!




Manager
Joined: 01 Feb 2010
Posts: 236

Re: please help me set up the equation for this problem
[#permalink]
Show Tags
27 Mar 2010, 04:17
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome 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 xy  monthly expenditure given, 12y = 3(xy) => x = 5y to calculate, y/x = 1/5 hence D



Manager
Joined: 12 Feb 2012
Posts: 125

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
27 Mar 2012, 18:30
Bunuel: A heart as pure as gold and a mind as sharp as a knife.



Intern
Joined: 19 Jan 2014
Posts: 26

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
03 Jul 2014, 18:36
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome 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.



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
04 Jul 2014, 03:02
bytatia wrote: changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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 DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
04 Jul 2014, 03:37
bytatia wrote: changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome 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
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 30 Sep 2014
Posts: 6

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
02 Nov 2014, 13:00
Hi GMAT club members, I tried to solve this problem as follows. Asume her monthly take home pay is x, and she saves 1/2x. Then the portion she did not save is 1/2x. Setting up the equation: 1/2x x 12 = 3(1/2x) 6x = 3/2x Then I get a ratio of 1/4.
Could someone please explain why my approach is wrong?
Thank you



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
03 Nov 2014, 02:42
sassy10 wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome pay did she save each month?
Hi GMAT club members, I tried to solve this problem as follows. Asume her monthly take home pay is x, and she saves 1/2x. Then the portion she did not save is 1/2x. Setting up the equation: 1/2x x 12 = 3(1/2x) 6x = 3/2x Then I get a ratio of 1/4.
Could someone please explain why my approach is wrong?
Thank you Hi, Notice that 6x does NOT equal to 3/2*x, so 6x = 3/2*x is not correct. You cannot arbitrarily assume here that she saves half of her take home pay. The fraction of the savings is fixed so 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 takehome pay that she did NOT save.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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 DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 08 Feb 2014
Posts: 205
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
11 Dec 2014, 08:01
Bunuel wrote: \(12s=3(ps)\) > \(s=p\frac{1}{5}\)
.
How do we solve this? I'm getting something different? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
11 Dec 2014, 08:03



Manager
Joined: 08 Feb 2014
Posts: 205
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
11 Dec 2014, 08:09
My apologies, I should have let this sit for a day and come back to it. I was subtracting 3s from 12s, instead of adding. Thanks again.



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
11 Dec 2014, 08:13



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
06 Dec 2016, 10:22
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome pay did she save each month?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6 Responding to a pm: Let monthly take home be 100 and the fraction she saves be x. 12*100*x = 3*100*(1x) 4x = 1  x x = 1/5 Answer (D)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
09 Feb 2017, 17:31
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome pay did she save each month?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6 We are given Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome pay each month. 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 takehome pay that she did not save we know that: 12S = 3N 4S = N We need to determine what fraction of her takehome 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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 08 Dec 2015
Posts: 298

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
14 Feb 2017, 11:41
Why isn't the equation 12y = (3(xy))*12 since we are told that this is the amount by the end the year? So 12 months accumulated.



CEO
Joined: 12 Sep 2015
Posts: 3021
Location: Canada

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
14 Feb 2017, 12:21
changhiskhan wrote: Alice’s takehome pay last year was the same each month, and she saved the same fraction of her takehome 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 takehome pay that she did NOT save. If all the money that she saved last year was from her takehome pay, what fraction of her takehome pay did she save each month?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 1/6 Here's another algebraic approach. 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 = 12 fM Important: If f = the fraction used to calculate monthly savings, then 1f = the fraction used to calculate amount not saved The means that (1f)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: 12 fM = 3 (1f)MNow solve for f Expand to get: 12fM = 3M  3fM Simplify: 15fM = 3M Divide both sides by 15M to get: f = 3M/15M = 1/5 Answer: D Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
15 Feb 2017, 02:48
iliavko wrote: Why isn't the equation 12y = (3(xy))*12 since we are told that this is the amount by the end the year? So 12 months accumulated. Note here what the question says: 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 takehome pay that she did NOT save. 3 times the amount of the monthly pay fraction, not the total annual pay fraction. So you do not multiply by 12.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)

Re: Alice’s takehome pay last year was the same each month, and
[#permalink]
Show Tags
09 Feb 2018, 12:21
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 Final Answer: 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
CoFounder & 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!*****




Re: Alice’s takehome pay last year was the same each month, and &nbs
[#permalink]
09 Feb 2018, 12:21



Go to page
1 2
Next
[ 32 posts ]



