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

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Intern
Joined: 17 Jan 2012
Posts: 41
GMAT 1: 610 Q43 V31
Henry purchased 3 items during a sale. He received a 20 [#permalink]

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Updated on: 08 Mar 2015, 13:29
4
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25
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Difficulty:

65% (hard)

Question Stats:

57% (01:09) correct 43% (01:00) wrong based on 945 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 [Reveal] Spoiler: Attachment: Henry discount on items.GIF [ 14.71 KiB | Viewed 15608 times ] [Reveal] Spoiler: OA Originally posted by docabuzar on 27 Jan 2012, 06:24. Last edited by Bunuel on 08 Mar 2015, 13:29, edited 3 times in total. Added the OA Math Expert Joined: 02 Sep 2009 Posts: 44598 Re: Henry purchased 3 items during a sale. He received a 20 [#permalink] ### Show Tags 27 Jan 2012, 06:32 13 This post received KUDOS Expert's post 25 This post was BOOKMARKED 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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Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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27 Jan 2012, 07:21
Then it makes sense. Thanks
Intern
Joined: 17 Jan 2012
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GMAT 1: 610 Q43 V31
Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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

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27 Jan 2012, 07:30
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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Joined: 17 Jan 2012
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Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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27 Jan 2012, 07:34
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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Posts: 44598
Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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

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

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23 Aug 2014, 12:21
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Expert's post
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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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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Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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19 Dec 2017, 00:35
Fortunately or Unfortunately, the OA is C for this one. I'm staring at the answer on GMATPREP software :/ Attaching screenshot
Attachments

Henry Purchased 3 items.docx [823.94 KiB]

Math Expert
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Posts: 44598
Re: Henry purchased 3 items during a sale. He received a 20 [#permalink]

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19 Dec 2017, 00:47
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] 19 Dec 2017, 00:47
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