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# Book and Hat

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Manager
Joined: 13 Mar 2009
Posts: 191

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15 May 2009, 01:20
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Ken withdrew \$200 in cash from the bank. Using the cash, he bought a book for exactly p dollars and a hat for exactly q dollars, where p and q are two-digit integers that have the same digits but in reverse order. Assuming no sales tax, each of the following could be the amount of cash, in dollars, that Ken has remaining EXCEPT:

(A) 79
(B) 90
(C) 113
(D) 145
(E) 167

OA will be posted later.
Senior Manager
Joined: 08 Jan 2009
Posts: 317

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15 May 2009, 02:26
Total Cash = 200 \$
p = xy = 10 x + y
q = yx = 10y + x

p + q = 11 ( x + y)

Remaining cash = 200 - 11 (x + y) where x+y = 1, 2 .....

200 - 11( 3 ) = 167
200 - 11( 55) = 145
200 - 11( 10) = 90
200 - 11( 11) = 79

So our Ans . C
Re: Book and Hat   [#permalink] 15 May 2009, 02:26
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