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How much less does a map sell for than a book?

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How much less does a map sell for than a book?

by gmatpup » Wed Nov 09, 2011 4:23 am
Can someone please give me a quick way to do this question:

A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $38, and on Tuesday the store sold 20 maps and 15 books for a total of $60. At this store, how much less does a map sell for than a book?

A. $0.25

B. $0.50

C. $0.75

D. $1.00

E. $1.25


Answer is B
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by Anurag@Gurome » Wed Nov 09, 2011 4:40 am
gmatpup wrote:A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $38, and on Tuesday the store sold 20 maps and 15 books for a total of $60. At this store, how much less does a map sell for than a book?
Say, price of a map is $M and price of a book is $B. Hence, we need to find (B - M).

Hence, 12M + 10B = 38 ....... (1)
And, 20M + 15B = 60 .......... (2)

Multiply (1) with 3 and (2) with 2 and their difference, (40M - 36M) = (2*60 - 3*38)
--> 4M = (2*60 - 3*38)
--> M = (2*15 - 3*9.5) = 1.5

Put M = 1.5 in (1), 12*1.5 + 10B = 38
--> 10B = 38 - 18 = 20
--> B = 2

Hence, (B - M) = 2 - 1.5 = 0.5

The correct answer is B.
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by GMATGuruNY » Wed Nov 09, 2011 7:58 am
gmatpup wrote:Can someone please give me a quick way to do this question:

A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $38, and on Tuesday the store sold 20 maps and 15 books for a total of $60. At this store, how much less does a map sell for than a book?

A. $0.25

B. $0.50

C. $0.75

D. $1.00

E. $1.25


Answer is B
Here is an alternate approach:

12M + 10B = 38.
Thus, if we buy 6 more maps and 5 more books -- increasing each number by half -- the total cost will increase by half ($19):
18M + 15B = 57.

The second given equation -- 20M + 15B = 60 -- is almost identical to the equation above, but it includes 2 additional maps and a cost increase of $3.
Thus, the 2 additional maps must account for the cost increase:
2M = 3
M = 1.5.

Substituting M=1.5 into the second given equation:.
20(1.5) + 15B = 60.
B = 2.

Thus, B-M = 2-1.5 = .5.

The correct answer is B.
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