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.
If the total price for n copies of a book is $31.5, what is
This topic has expert replies
-
- Moderator
- Posts: 2205
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$? = c\,\,\left( {{\rm{dollar}}\,\,{\rm{cost}}\,\,{\rm{per}}\,\,{\rm{copy}}} \right)$$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.
$$n \cdot c = 31.5\,\,\,\,\left[ \$ \right]\,\,\,\,\,\,\left( * \right)$$
$$\left( 1 \right)\,\,2n \cdot 1.75 = 31.5\,\,\,\, \Rightarrow \,\,\,n\,\,{\rm{unique}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,? = c\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( {\,{\rm{POST - MORTEM}}\,\,:\,\,\,\,c\,\,\mathop = \limits^{\left( * \right)} \,\,{{31.5} \over n} = 2 \cdot 1.75\,} \right)$$
$$\left( 2 \right)\,\,\left( {n - 4} \right)\left( {c + 2.8} \right) = 31.5\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left( {{{31.5} \over c} - 4} \right)\left( {c + 2.8} \right) = 31.5$$
$$31.5 = 31.5 + {{\left( {31.5} \right)\left( {2.8} \right)} \over c} - 4c - 4 \cdot 2.8\,\,\,\,\, \Rightarrow \,\,\,\,\,4{c^2} + 4 \cdot 2.8 \cdot c - \left( {31.5} \right)\left( {2.8} \right) = 0$$
$${c_1}{c_2} = {{ - \left( {31.5} \right)\left( {2.8} \right)} \over 4} < 0\,\,\,\,\left( {{c_1},{c_2}\,\,{\rm{roots}}} \right)\,\,\,\,\, \Rightarrow \,\,\,c > 0\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,{\rm{SUFF}}.$$
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
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br