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Alex paid a $12 fee to receive a 10% discount off of the

by BTGmoderatorDC » Sat Sep 01, 2018 11:25 pm

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Alex paid a $12 fee to receive a 10% discount off of the list price on all books he bought in a six-month period. Victor paid a $15 fee to receive a 15% discount off of the list price on all books he bought in the same period. If each bought books with a total list price of b during that period and each paid the same net amount, including the discount and the fee, what is b ?

A. $54
B. $60
C. $66
D. $100
E. $120

OA B

Source: Princeton Review
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by [email protected] » Sun Sep 02, 2018 7:49 pm
Hi All,

We're told that Alex paid a $12 fee to receive a 10% discount off of the list price on all books he bought in a six-month period and Victor paid a $15 fee to receive a 15% discount off of the list price on all books he bought in the same period. We're told that EACH person bought books with a total list price of $B during that period and each paid the SAME net amount, including the discount and the fee. We're asked for the value of B. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

Since Alex and Victor paid the SAME overall total for the books, the difference in the discounts (10% vs. 15%) has to 'offset' the difference in fees ($12 vs. $15). Since the difference in fees is relatively small, it's likely that we're dealing with a value of B that is also relatively small. Let's TEST Answer B first...

Answer B: $60
IF... the total spent on books was $60...
Alex paid $60 - (.1)($60) + $12 = 54 + 12 = $66 in total
Victor paid $60 - (.15)($60) + $15 = 51 + 15 = $66 in total
These two totals are equal, so this MUST be the answer.

Final Answer: B

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Rich
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by Brent@GMATPrepNow » Mon Sep 03, 2018 5:17 am
BTGmoderatorDC wrote:Alex paid a $12 fee to receive a 10% discount off of the list price on all books he bought in a six-month period. Victor paid a $15 fee to receive a 15% discount off of the list price on all books he bought in the same period. If each bought books with a total list price of b during that period and each paid the same net amount, including the discount and the fee, what is b ?

A. $54
B. $60
C. $66
D. $100
E. $120

OA B

Source: Princeton Review
IMPORTANT:
If Alex received a 10% discount, then Alex PAID 90% of the cost of the books
If Victor received a 15% discount, then Victor PAID 85% of the cost of the books

Start with a word equation

Total amount Alex paid = Total amount Victor paid
We get: $12 + 90% of b = $15 + 85% of b
Rewrite as: $12 + (0.9)(b) = $15 + (0.85)(b)
Eliminate decimals by multiplying both sides by 100 to get: 1200 + 90b = 1500 + 85b
Subtract 1200 from both sides: 90b = 300 + 85b
Subtract 85b from both sides: 5b = 300
Solve: b = 60

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Fri Sep 07, 2018 4:20 pm
BTGmoderatorDC wrote:Alex paid a $12 fee to receive a 10% discount off of the list price on all books he bought in a six-month period. Victor paid a $15 fee to receive a 15% discount off of the list price on all books he bought in the same period. If each bought books with a total list price of b during that period and each paid the same net amount, including the discount and the fee, what is b ?

A. $54
B. $60
C. $66
D. $100
E. $120
We can create the equation:

12 + 0.9b = 15 + 0.85b

0.05b = 3

b = 60

Answer: B

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by swerve » Sat Sep 08, 2018 8:50 am
$$12+\frac{90b}{100}=15+\frac{85b}{100}...$$
(90% value was paid as discount is 10%... on similar lines 85%)
$$\frac{5b}{100}=3\quad\Rightarrow\quad b=60$$
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