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
Mike has twice as many stamps as Jean has. After he gives
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 ceilidh.erickson
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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 >
\(M6=(J+6)+8\)
*NB: remember that in an EXCHANGE problem, when he gives her 6 stamps, he loses 6 stamps (M6) but she also gains 6 stamps (J+6).
Now simplify the 2nd equation:
\(M6=(J+6)+8\)
\(M6=J+14\)
\(J=M20\)
Now substitute this in for J in the 1st equation to solve for M:
\(M=2J\)
\(M=2(M20)\)
\(M=2M40)\)
\(M=40\)
The answer is E.
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 >
\(M6=(J+6)+8\)
*NB: remember that in an EXCHANGE problem, when he gives her 6 stamps, he loses 6 stamps (M6) but she also gains 6 stamps (J+6).
Now simplify the 2nd equation:
\(M6=(J+6)+8\)
\(M6=J+14\)
\(J=M20\)
Now substitute this in for J in the 1st equation to solve for M:
\(M=2J\)
\(M=2(M20)\)
\(M=2M40)\)
\(M=40\)
The answer is E.
Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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GMAT/MBA Expert
 ceilidh.erickson
 GMAT Instructor
 Posts: 2094
 Joined: 04 Dec 2012
 Thanked: 1443 times
 Followed by:242 members
This type of 2variable 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).
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
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!