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Henry purchased 3 items during a sale. He received a 20 percent discou
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Updated on: 11 Jun 2019, 03:53
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Difficulty:
55% (hard)
Question Stats:
66% (02:20) correct 34% (02:26) wrong based on 650 sessions
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Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15
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27 Jan 2012, 06:32
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docabuzar wrote:
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20 (2) The regular price of the least expensive item was $15
Let the prices be a, b, and c, so that a > b > c.
Basically the questions: is \(0.2a+0.1b+0.1c>0.15(a+b+c)\)? --> is \(a>b+c\)?
(1) The regular price of the most expensive item was $50 and the regular price of the next most expensive item was $20 --> \(a=50\), \(b=20\), \(c\leq{20}\) (as the second most expensive item was $20 then the least expansive item, the third one, must be less than or equal to 20). So the question becomes: is \(50>20+c\) --> is \(c<30\)? As we got that \(c\leq{20}\), hence the above is always true. Sufficient.
(2) The regular price of the least expensive item was $15. Clearly insufficient.
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27 Jan 2012, 07:25
THe Q asks for the which of discounts will be greater 20%, 10%, 10% on A, B, C resp or 15% on (A+B+C). How can we say its same as 50> 20+C ? Now I m totally lost.
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27 Jan 2012, 07:30
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docabuzar wrote:
THe Q asks for the which of discounts will be greater 20%, 10%, 10% on A, B, C resp or 15% on (A+B+C). How can we say its same as 50> 20+C ? Now I m totally lost.
The questions asks: is \(0.2a+0.1b+0.1c>0.15(a+b+c)\)? After simplifying we'll get that the question becomes: is \(a>b+c\)?
(1) says \(a=50\) and \(b=20\). Also we concluded that: \(c\leq{20}\). Now, if we substitute the values of a and b we'll get that the question boils down to: is \(50>20+c\)? or is \(c<30\)?
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27 Jan 2012, 07:38
docabuzar wrote:
Thanks. Its clear now.
Just how do you know to keep A on one side & B & C on other? This simplied the Ans a lot.
It really doesn't matter how you write it: \(a>b+c\), \(a-b-c>0\), \(a-b>c\), ... You still will get the same result. For me \(a>b+c\) was the most "attractive" form, so I chose this one.
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22 Aug 2014, 20:30
Bunuel: if the first item is 50, the next 2 are 20. If I take 20% of 50 I get 10 and 10% of 20 I get 2. Total discount is 14 and total price is 90. 14/90>.15. What's am I doing wrong?
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23 Aug 2014, 12:21
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bankerboy30 wrote:
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20 (2) The regular price of the least expensive item was $15
Bunuel: if the first item is 50, the next 2 are 20. If I take 20% of 50 I get 10 and 10% of 20 I get 2. Total discount is 14 and total price is 90. 14/90>.15. What's am I doing wrong?
Total discount = $14. The sum of the regular prices of the 3 items = $90. 15% of $90 = $13.5.
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15 Jul 2017, 11:24
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I believe this question is a perfect example of an "Easy C" trap. Just by realizing that A&B would be sufficient and make the problem way too easy, we can eliminate C,D and E. This is a simple rule that could improve one's chances on 700+ problems
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11 Jun 2019, 03:51
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66% (02:20) correct 
Thanks
