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tagged by: BTGmoderatorLU

## If the total price for n copies of a book is $31.5, what is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Princeton Review If the total price for n copies of a book is$31.5, what is the price per copy of the book?

1) If twice as many copies were bought for the same total price, the price per copy would be $1.75. 2) If 4 fewer copies were bought for the same total price, the price per copy would be$2.80 greater.

The OA is D.

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BTGmoderatorLU wrote:
Source: Princeton Review

If the total price for n copies of a book is $31.5, what is the price per copy of the book? 1) If twice as many copies were bought for the same total price, the price per copy would be$1.75.
2) If 4 fewer copies were bought for the same total price, the price per copy would be $2.80 greater. $$? = c\,\,\left( {{\rm{dollar}}\,\,{\rm{cost}}\,\,{\rm{per}}\,\,{\rm{copy}}} \right)$$ $$n \cdot c = 31.5\,\,\,\,\left[ \ \right]\,\,\,\,\,\,\left( * \right)$$ $$\left( 1 \right)\,\,2n \cdot 1.75 = 31.5\,\,\,\, \Rightarrow \,\,\,n\,\,{\rm{unique}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,? = c\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}{\rm{.}}$$ $$\left( {\,{\rm{POST - MORTEM}}\,\,:\,\,\,\,c\,\,\mathop = \limits^{\left( * \right)} \,\,{{31.5} \over n} = 2 \cdot 1.75\,} \right)$$ $$\left( 2 \right)\,\,\left( {n - 4} \right)\left( {c + 2.8} \right) = 31.5\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left( {{{31.5} \over c} - 4} \right)\left( {c + 2.8} \right) = 31.5$$ $$31.5 = 31.5 + {{\left( {31.5} \right)\left( {2.8} \right)} \over c} - 4c - 4 \cdot 2.8\,\,\,\,\, \Rightarrow \,\,\,\,\,4{c^2} + 4 \cdot 2.8 \cdot c - \left( {31.5} \right)\left( {2.8} \right) = 0$$ $${c_1}{c_2} = {{ - \left( {31.5} \right)\left( {2.8} \right)} \over 4} < 0\,\,\,\,\left( {{c_1},{c_2}\,\,{\rm{roots}}} \right)\,\,\,\,\, \Rightarrow \,\,\,c > 0\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}.$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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