Alice and Bruce each bought a refrigerator...

Expert replies

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon Oct 02, 2017 9:42 am

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.

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 02, 2017 9:42 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 02, 2017 9:55 am

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

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 02, 2017 10:20 am

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

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sun Oct 08, 2017 8:10 am

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.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sat Sep 29, 2018 4:58 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 30, 2018 3:56 pm

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

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review