This question really confused me. I know the strategy for it is to pick "smart numbers" to stand in for the unknown incomes, but is there some way to do it if you kept them as unknowns? It seems like you should be able to figure out the fraction of their combined monthly income if you know what fraction of their monthly income each of them have to donate. I guess they key here is that the problem tells you that Carrie earns twice as much? If you didn't know that, would it be possible to solve this problem?
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate,
Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent
and 1/2 on food. If the two women decide to donate the remainder of their money
to charity each month, what fraction of their combined monthly income will they
donate?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Smart Numbers Problem
This topic has expert replies
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's start with the "smart numbers" approach.jroach31 wrote: Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate,
Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent
and 1/2 on food. If the two women decide to donate the remainder of their money
to charity each month, what fraction of their combined monthly income will they
donate?
We want some salaries that work well with the fractions 5/12, 3/8, 1/4 and 1/2.
The LEAST COMMON MULTIPLE of 12, 8, 4 and 2 is 24, so let's say that Lisa earns $24/month.
Since Carrie earns twice as much as Lisa, Carrie earns $48/month.
LISA
Paycheck: $24
Rent = 3/8 of $24 = $9
Food = 5/12 of $24 = $10
So, charity = $24 - $9 - $10
= $5
CARRIE
Paycheck: $48
Rent = 1/4 of $48 = $12
Food = 1/2 of $48 = $24
So, charity = $48 - $12 - $24
= $12
Combined paychecks = $24 + $48 = $72
Combined charity = $5 + $12 = $17
So, fraction of combined income that goes to charity = 17/72
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's the algebraic approach.jroach31 wrote: Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate,
Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent
and 1/2 on food. If the two women decide to donate the remainder of their money
to charity each month, what fraction of their combined monthly income will they
donate?
Let x = Lisa's monthly paycheck
So 2x = Carrie's monthly paycheck
LISA
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food
Fraction for charity = 1 - 3/8 - 5/12 = 24/24 - 9/24 - 10/24 = 5/24
Amount given to charity = 5/24 of x = 5x/24
CARRIE
Carrie spends 1/4 of her monthly paycheck on rent and 1/2 on food
Fraction for charity = 1 - 1/4 - 1/2 = 4/4 - 1/4 - 2/4 = 1/4
Amount given to charity = 1/4 of 2x = 2x/4 = x/2
Combined paychecks = x + 2x = 3x
Combined charity = 5x/24 + x/2 = 5x/24 + 12x/24 = 17x/24
So, fraction of combined income that goes to charity = (17x/24)/3x = 17/72
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Exactly.jroach31 wrote:One additional question...if you weren't given the ratio of Lisa's income to Carrie's income, you wouldn't be able to solve this, right?
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi jroach31,
Brent's explanation that focused on TESTing Values is a great approach to learn and master. It's a tactic that is easy to use and can be used on many GMAT Quant questions.
As to your last question, if you weren't given the ratio of the two incomes, there IS a way to solve this problem using algebra, but the solution would not be as pretty:
Lisa spends 3/8 on rent and 5/12 on food, so she spends 9/24 + 10/24 = 19/24 of her paycheck
She would end up giving 5X/24 to charity
Carrie spends 1/4 on rent and 1/2 on food, so she spends 1/4 + 2/4 = 3/4 of her paycheck
She would end up giving 1Y/4 to charity
The total that the two women would have given to charity = 5X/24 + Y/4
If we go one more step and create a common denominator, we'd have:
5X/24 + 6Y/24
(5X + 6Y)/24
GMAT assassins aren't born, they're made,
Rich
Brent's explanation that focused on TESTing Values is a great approach to learn and master. It's a tactic that is easy to use and can be used on many GMAT Quant questions.
As to your last question, if you weren't given the ratio of the two incomes, there IS a way to solve this problem using algebra, but the solution would not be as pretty:
Lisa spends 3/8 on rent and 5/12 on food, so she spends 9/24 + 10/24 = 19/24 of her paycheck
She would end up giving 5X/24 to charity
Carrie spends 1/4 on rent and 1/2 on food, so she spends 1/4 + 2/4 = 3/4 of her paycheck
She would end up giving 1Y/4 to charity
The total that the two women would have given to charity = 5X/24 + Y/4
If we go one more step and create a common denominator, we'd have:
5X/24 + 6Y/24
(5X + 6Y)/24
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
-
Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can let p = Lisa's monthly paycheck. Thus, Carrie's monthly paycheck = 2p. Now we can determine each person's rent expense, food expense, and remaining money in terms of p.jroach31 wrote:
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their moneyto charity each month, what fraction of their combined monthly income will they
donate?
Lisa:
Rent = (3/8)p
Food = (5/12)p
Remainder = p - (3/8)p - (5/12)p = (24/24)p - (9/24)p - (10/24)p = (5/24)p
Carrie:
Rent = (1/4)(2p) = (1/2)p
Food = (1/2)(2p) = p
Remainder = 2p - (1/2)p - p = (1/2)p
From the above, we see that the combined money they donate to charity is the sum of their remaining money:
(5/24)p + (1/2)p = (5/24)p + (12/24)p = (17/24)p
Also, the combined money they earn in a month is p + 2p = 3p.
Thus, the fraction of their monthly income donated to charity is [(17/24)p]/(3p) = (17/24)/3 = 17/72.
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
