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Alice and Bruce each bought a refrigerator...

by Vincen » Mon Oct 02, 2017 9:42 am

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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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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
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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
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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.
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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

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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

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Rich
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