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

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Intern
Joined: 27 Mar 2009
Posts: 12
Henry purchased 3 items during a sale. He received a 20 [#permalink]

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05 Apr 2009, 08:28
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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 of 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.

A or D....?? DS question.. in prep its
[Reveal] Spoiler: OA:
Director
Joined: 29 Aug 2005
Posts: 836

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06 Apr 2009, 11:15
1. Please, post in relevant folder
2. Dont post the OA with the question.

Now to the question:
x>y>z
0.2x+0.1y+0.1z>0.15(x+y+z)?

Stmt1: x=50; y=20 (implies: z<20 - lets denote it as "LT20")
0.2*50+0.1*20+0.1*LT20>0.15(50+20+LT20)?
10+2+LT2>7.5+3+LT3?
LT14>LT14.5?
Both sides of the inequality are less than 14 and 14.5 by the same amount.
We can answer the question and it is "definately no". Sufficient.

Stmt: z=15
This is not suff.

Hence, A.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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06 Apr 2009, 16:37
botirvoy wrote:
1. Please, post in relevant folder
2. Dont post the OA with the question.

Now to the question:
x>y>z
0.2x+0.1y+0.1z>0.15(x+y+z)?

Stmt1: x=50; y=20 (implies: z<20 - lets denote it as "LT20")
0.2*50+0.1*20+0.1*LT20>0.15(50+20+LT20)?
10+2+LT2>7.5+3+LT3?
LT14>LT14.5?
Both sides of the inequality are less than 14 and 14.5 by the same amount.
We can answer the question and it is "definately no". Sufficient.

I think you might have invented some new math along with your new notation "LT20"! Let's call that z instead, and rephrase the question, using the equation you set up:

Is 0.2*50+0.1*20+0.1*z > 0.15(50+20+z) ?
Is 10 + 2 + 0.1z > 7.5 + 3 + 0.15z ?
Is 1.5 > 0.05z ?
Is 30 > z ?

That is, the question is just asking whether we can be certain that z is less than 30. Since we know z is less than 20, Statement 1 is sufficient on its own, and the answer is a definite 'yes'.

Alternatively, you could recognize that this is just a weighted average question - the average discount will be weighted by the prices. If the item with the 20% discount costs \$50, and the items with the 10% discount cost less than \$50, the overall discount must be closer to 20% than to 10%. Statement 1 guarantees that.
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Manager
Joined: 19 Aug 2006
Posts: 233

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06 Apr 2009, 19:38
I solved it wrong at first, but then reread the question and solved it just like the previous poster above.
Agree with A.

stmnt 2 - insuffic.
Intern
Joined: 05 Jun 2007
Posts: 48
Schools: CMU, Ross, Kellogg, Case, OSU, Stanford, Kelley

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14 Apr 2009, 13:02
The ans is A..
stmt 2 is insuff to solve the q
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 607

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22 Apr 2009, 12:50

http://www.gmatquantum.com/shared-posts ... blem7.html

The original question is not included in the video because of copyright issues.

Dabral

zaz wrote:
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item of 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.

____A or D....?? DS question.. in prep its answer is A...!!
Re: ds: A/D...??   [#permalink] 22 Apr 2009, 12:50
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