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Arithmetic

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by sud21 » Fri Oct 09, 2015 8:05 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
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by GMATinsight » Fri Oct 09, 2015 8:44 pm
sud21 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
Let, Amounts of Money spent by Four friends, Charles, Mike, Brian, and John are C, M, B and J respectively

M = B + 400--------------Eq(1)
J = C - 1200--------------Eq(2)
C = M + 400--------------Eq(3)
B - J = ?

Substituting the value of C from Eq(3) in Eq(2)

J = (M+400) - 1200
i.e. J = M - 800
i.e. M = J + 800

Substituting the value of M in Eq(1)

J + 800 = B + 400
i.e. B - J = 800-400 = 400

Answer: option A
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by [email protected] » Fri Oct 09, 2015 9:59 pm
Hi sud21,

While most Test Takers would approach this question with Algebra, it can actually be solved rather easily by TESTing VALUES.

We're never given any limitations on how much total money is actually spent, so the individual values (and the total) can be ANYTHING, as long as the values relate to one another as described. So, working through the information that is provided....

IF....
Brian = $1,000
Mike spent $400 more than Brian....

Mike = $1,400

John spent $1,200 less than Charles (we'll come back to this in a moment)

Charles spent $400 more than Mike...
Charles = $1,800

Now, back to the prior info - John spent $1,200 less than Charles...
John = $600

The question asks how many MORE dollars Brian spent than John:
Brian = $1,000
John = $600
$1,000 - $600 = $400

Final Answer: A

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