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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Alice and Bruce each bought a refrigerator... tagged by: Brent@GMATPrepNow ##### This topic has 5 expert replies and 0 member replies ## Alice and Bruce each bought a refrigerator... Alice and Bruce each bought a refrigerator, and the sum of their purchases was$900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator? A.$275
B. $325 C.$425
D. $575 E.$625

The OA is B.

I didn't know how to set the equations to solve the problem. I need some help here. Thanks.

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Vincen wrote:
Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was$75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275 B.$325
C. $425 D.$575
E. $625 This question lends itself nicely to testing the answer choices We'll start with answer choice C ($425), the middle value.
If Alice paid $425, how much did Bruce pay? Given: twice of what Alice paid was$75 more than what Bruce paid
Two times $425 =$850, so Bruce paid $775 (since$850 - $75 =$775
COMBINED PAYMENTS = $425 +$775 = $1200 No good - we need the combined payments to be$900
ELIMINATE C
We can also ELIMINATE D and E, because those values will yield an even greater values of the combined payments.

Now let's try B ($325) Given: twice of what Alice paid was$75 more than what Bruce paid
Two times $325=$650, so Bruce paid $575 (since$650 - $75 =$575
COMBINED PAYMENTS = $325 +$575 = $900 Perfect!!! Answer: B Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12743 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 Vincen wrote: Alice and Bruce each bought a refrigerator, and the sum of their purchases was$900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator? A.$275
B. $325 C.$425
D. $575 E.$625
We can also solve the question algebraically, using 1 variable or 2 variables.
Here's a solution with 1 variable:

Given: Twice of what Alice paid was $75 more than what Bruce paid Let x = the amount Alice paid So, 2x - 75 = the amount Bruce paid Given: The sum of their purchases was$900
So, (the amount Alice paid) + (the amount Bruce paid) = 900
We get: x + (2x - 75) = 900
Simplify: 3x - 75 = 900
Solve: x = 325

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Sign up for our free Question of the Day emails
And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

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Vincen wrote:
Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was$75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275 B.$325
C. $425 D.$575
E. $625 The OA is B. I didn't know how to set the equations to solve the problem. I need some help here. Thanks. Hi Vincen, Let's take a look at your question. The question states that, Alice and Bruce each bought a refrigerator, and the sum of their purchases was$900.
Let 'x' be the amount Alice paid and 'y' be the amount Bruce paid for the purchase. Then,
x + y = 900 ----- (i)

Also, twice of what Alice paid was $75 more than what Bruce paid can be represented as, 2x = y + 75 y = 2x - 75 ----- (ii) Plugin y = 2x - 75 in (i), x + y = 900 x + 2x - 75 = 900 3x = 900 + 75 3x = 975 x = 975/3 x = 325 Since 'x' is the amount Alice paid for his purchase, therefore, Alice paid$325 for her refrigerator.

Therefore, Option B is correct.

I am available if you'd like any followup.

_________________
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Vincen wrote:
Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was$75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275 B.$325
C. $425 D.$575
E. $625 We can let a = the amount Alice paid for her refrigerator and b = the amount Bruce paid for his refrigerator. Therefore, a + b = 900 and 2a = b + 75 Isolating b in the second equation, we have b = 2a - 75. Substituting this for b in the first equation, we have: a + 2a - 75 = 900 3a = 975 a = 325 Answer: B ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10111 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that Alice and Bruce each bought a refrigerator, and the sum of their purchases was$900. We're also told that TWICE of what Alice paid was $75 MORE than what Bruce paid. We're asked what did Alice paid for her refrigerator. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. To start, as an estimate, if Bruce paid exactly twice what Alice paid, then their two purchase prices would have been 600 and 300, respectively. However, we know that that did NOT happen (since "twice what Alice paid was$75 MORE than what Bruce paid"). Thus, Alice would have paid a bit more than $300. Let's TEST Answer B first... Answer B:$325
IF.... Alice paid $325, then Bruce paid 2($325) - $75 =$650 - $75 =$575
Total paid by both = $325 +$575 = $900 This is an exact match for what we were told, so this MUST be the answer. Final Answer: B GMAT assassins aren't born, they're made, Rich • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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