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
Alex paid a $12 fee to receive a 10% discount off of the
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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IMPORTANT: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
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
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We can create the equation: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
12 + 0.9b = 15 + 0.85b
0.05b = 3
b = 60
Answer: B
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