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Four friends, Charles, Mike, Brian, and John, went on a...

by swerve » Sat Feb 10, 2018 7:02 am
Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?

A. $400
B. $600
C. $800
D. $1000
E. $1200

The OA is A.

If Mike spent $400 more than Brian, this can be written like M = B + 400 (1).

If John spent $1200 less than Charles, this can be written like J = C - 1200 (2).

If Charles spent $400 more than Mike, this can be written like C = M + 400 (3).

Then, I need to find how many more dollars did Brian spent than John, Can I write this like B - J = $?

From (1), B = M - 400

Then (1) - (2),

B - J = M - 400 - C + 1200 = M - C + 800 (4).

Then, (3) into (4), B -J = M - M - 400 + 800, finally, B - J = 400. Right?

Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by EconomistGMATTutor » Sat Feb 10, 2018 12:17 pm
Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?

A. $400
B. $600
C. $800
D. $1000
E. $1200

The OA is A.

If Mike spent $400 more than Brian, this can be written like M = B + 400 (1).

If John spent $1200 less than Charles, this can be written like J = C - 1200 (2).

If Charles spent $400 more than Mike, this can be written like C = M + 400 (3).

Then, I need to find how many more dollars did Brian spent than John, Can I write this like B - J = $?

From (1), B = M - 400

Then (1) - (2),

B - J = M - 400 - C + 1200 = M - C + 800 (4).

Then, (3) into (4), B -J = M - M - 400 + 800, finally, B - J = 400. Right?

Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
Hi swerve,
Let's take a look at your question.

The approach you used is absolutely correct. But we can solve it Just by adding up all three equations.
$$M=B+400\ ...\left(i\right)$$
$$J=C-1200\ ...\left(ii\right)$$
$$C=M+400...\left(iii\right)$$

Adding Eq(i), (ii) and (iii), we get:
$$M+J+C=B+400+C-1200+M+400$$
$$M+J+C=B+C+M-400$$
$$J=B-400$$
$$B-J=400$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
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by GMATGuruNY » Sat Feb 10, 2018 1:30 pm
swerve wrote:Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?

A. $400
B. $600
C. $800
D. $1000
E. $1200
Mike spent $400 more than Brian did.
Let B=1000, implying that M = 1000+400 = 1400.

Charles spent $400 more than Mike did.
Since M=1400, C = 1400+400 = 1800.

John spent $1200 less than Charles did.
Since C=1800, J = 1800-1200 = 600.

How many more dollars did Brian spend than John did?
B-J = 1000-600 = 400.

The correct answer is A.
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by Scott@TargetTestPrep » Sun Jun 23, 2019 6:27 pm
swerve wrote:Four friends, Charles, Mike, Brian, and John, went on a shopping trip. If Mike spent $400 more than Brian did, John spent $1200 less than Charles did, and Charles spent $400 more than Mike did, how many more dollars did Brian spend than John did?

A. $400
B. $600
C. $800
D. $1000
E. $1200
We can create the equations:

M = B + 400

and

J = C - 1200

and

C = M + 400

Adding equations 2 and 3, we have:

J + C = C + M - 800

J = M - 800

Adding M = B + 400 and J = M - 800, we have:

M + J = B + M - 400

J = B - 400

J + 400 = B

We see that Brian spent $400 more than John.

Answer: A

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