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Henry purchased 3 items during a sale. He received a 20

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Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post Updated on: 08 Mar 2015, 12:29
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Question Stats:

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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

Attachment:
Henry discount on items.GIF
Henry discount on items.GIF [ 14.71 KiB | Viewed 18228 times ]

Originally posted by docabuzar on 27 Jan 2012, 05:24.
Last edited by Bunuel on 08 Mar 2015, 12:29, edited 3 times in total.
Added the OA
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 05:32
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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.

Answer: A.
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 06:21
Then it makes sense. :) Thanks
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 06:25
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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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 06:30
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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 \(c<30\)?

Hope it's clear.
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 06:34
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.
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 27 Jan 2012, 06:38
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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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 22 Aug 2014, 19:30
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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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 23 Aug 2014, 11:21
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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.

$14 > $13.5.
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 15 Jul 2017, 10:24
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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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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 18 Dec 2017, 23:35
Fortunately or Unfortunately, the OA is C for this one. I'm staring at the answer on GMATPREP software :/ Attaching screenshot
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 18 Dec 2017, 23:47
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vishal205 wrote:
Fortunately or Unfortunately, the OA is C for this one. I'm staring at the answer on GMATPREP software :/ Attaching screenshot


The OA for the question discussed above is A, NOT C.

The question you attached is not the one discussed above, it's another one discussed here: https://gmatclub.com/forum/henry-purcha ... 94280.html
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Re: Henry purchased 3 items during a sale. He received a 20  [#permalink]

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New post 14 Jul 2018, 20:03
Bunuel wrote:
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.

Answer: A.



Where is it mentioned that b>c? both the items could've the same price or even c>b? No? Please correct me.
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Re: Henry purchased 3 items during a sale. He received a 20 &nbs [#permalink] 14 Jul 2018, 20:03
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