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Mike has twice as many stamps as Jean has. After he gives

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Mike has twice as many stamps as Jean has. After he gives Jean 6 stamps, he still has 8 more stamps than Jean does. How many stamps did Mike have originally?

A. 28
B. 32
C. 36
D. 38
E. 40

OA E

Source: Princeton Review

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by ceilidh.erickson » Sat Jun 01, 2019 10:45 am
We can easily translate this algebraically. Let M = Mike's original # of stamps, and J - Jean's original # of stamps.

Mike has twice as many stamps as Jean has -->
\(M=2J\)

After he gives Jean 6 stamps, he still has 8 more stamps than Jean does -->
\(M-6=(J+6)+8\)
*NB: remember that in an EXCHANGE problem, when he gives her 6 stamps, he loses 6 stamps (M-6) but she also gains 6 stamps (J+6).

Now simplify the 2nd equation:
\(M-6=(J+6)+8\)
\(M-6=J+14\)
\(J=M-20\)

Now substitute this in for J in the 1st equation to solve for M:
\(M=2J\)
\(M=2(M-20)\)
\(M=2M-40)\)
\(M=40\)

The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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by ceilidh.erickson » Sat Jun 01, 2019 10:51 am
This type of 2-variable word problem is know as an EXCHANGE problem, and it can be tricky. For more on exchange problems and translating other tricky word problems, here is a video lesson:
https://www.youtube.com/watch?v=5Kg6mjN ... ex=11&t=0s
(It's listed for the GRE, but the exam same types of tricky word problems appear on the GMAT and GRE).
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education