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Intern  Joined: 15 Oct 2014
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Henry purchased three items during a sale. He received a 20% discount  [#permalink]

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Question Stats: 74% (01:36) correct 26% (01:38) wrong based on 790 sessions

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Henry purchased three items during a sale. He received a 20% discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts?

(1) the average (arithmetic mean) of the regular prices of the 3 items was $30. (2) the regular price of the most expensive of the 3 items was$50

Originally posted by annaleroy on 08 Mar 2015, 13:21.
Last edited by Bunuel on 08 Mar 2015, 13:22, edited 1 time in total.
Renamed the topic and edited the question.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Henry purchased three items during a sale. He received a 20% discount  [#permalink]

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Hi annaleroy,

There are a couple of different ways to approach this question. Regardless of what method you choose, you will have to stay organized, take plenty of notes and do enough work to prove your answer. There's a great opportunity in this question to TEST VALUES and do a little arithmetic.

Here, we know that there are 3 items purchased. We know that the MOST EXPENSIVE ITEM got a 20% discount and the other 2 items got a 10% discount. We're asked for the TOTAL amount of the discounts.

Fact 1: The AVERAGE of the prices of the 3 items was $30. If the 3 items cost:$40, $30 and$20, then the TOTAL discount = $8 +$3 + $2 =$13
If the 3 items cost: $50,$30 and $10, then the TOTAL discount =$10 + $3 +$1 = $14 Fact 1 is INSUFFICIENT Fact 2: The most expensive item was$50

This tells us that the discount for that 1 item was (.2)($50) =$10, but we don't know the cost of the other 2 items, so we don't know what the discounts will be.
Fact 2 is INSUFFICIENT

Combining Facts though, we know…

1) The average of the 3 items is $30, so the SUM of the 3 items =$90
2) The most expensive item is $50, so the OTHER 2 items sum up to$40

(2) the regular price of the most expensive of the 3 items was $50 question asks: 0.9(x+y)+0.8z/(x+y+z) -> where x, y, z are products, and z is the most expensive one. 1. we can find x+y+z - but nothing else. 2. we know z, but nothing else. 1+2:z=50, x+y+z=90. we have everything we need to find the answer to the question. no need to solve Director  G Affiliations: CrackVerbal Joined: 03 Oct 2013 Posts: 563 Location: India GMAT 1: 780 Q51 V46 Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] Show Tags 1 Top Contributor Hi Annaleroy, While solving DS questions especially questions dealing with ratios, percentages or word problems it always makes sense to first deconstruct the question before evaluating the statements. Let the price of the most expensive item be 'x', Let the price of the next most expensive item be 'y' and Let the price of the least expensive item be 'z'. Since Henry received a 20% discount on the most expensive item, the discount is (20/100)x Since Henry received a 10% discount on the next most expensive item, the discount is (10/100)y and Since Henry received a 10% discount on the least expensive item, the discount is (10/100)z Now the question states 'What was the total amount of the 3 discounts'? Total discount = (20/100)x + (10/100)y + (10/100)z ------> (2x + y + z)/100 Statement 1 : the average (arithmetic mean) of the regular prices of the 3 items was$30.

(x + y + z)/3 = 30 ------> x + y + z = 90

this does not give us the value of 2x + y + z. So insufficient.

Statement 2 : the regular price of the most expensive of the 3 items was $50 Here we have x = 50. We do not have any information about y and z. Insufficient. Combining Statements 1 and 2 : From Statement 1 we have x + y + z = 90 and from statement 2 we have x = 50, so 2x + y + z can be split into x + x + y + z. Sufficient. Answer : C CrackVerbal Academics Team _________________ - CrackVerbal Prep Team For more info on GMAT and MBA, follow us on @AskCrackVerbal Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHq Register for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personal-tutoring/ Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2816 Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] Show Tags annaleroy wrote: Henry purchased three items during a sale. He received a 20% discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts? (1) the average (arithmetic mean) of the regular prices of the 3 items was$30.
(2) the regular price of the most expensive of the 3 items was $50 We are given that Henry received a 20% discount on the most expensive of the 3 items he purchased and a 10% discount on the other 2 items. We need to determine the total amount of the 3 discounts. We can let the most expensive item = a, one lesser expensive item = b, and the other lesser expensive item = c. Thus,we need to determine: 0.2a + 0.1b + 0.1c = ? 0.2a + 0.1(b + c) = ? Statement One Alone: The average (arithmetic mean) of the regular prices of the 3 items was$30.

Using the information in statement one, we can create the following equation:

(a + b + c)/3 = 30

a + b + c = 90

Since we don’t know the individual values of a, b and c (especially the value of a), statement one alone is not sufficient to answer the question.

Statement Two Alone:

The regular price of the most expensive of the 3 items was $50. Using the information in statement two, we know that a = 50 and thus 0.2(50) = 10. However, since we don’t know anything about b and c, we still do not have enough information to answer the question. Statements One and Two Together: Using statements one and two we know that a = 50 and that a + b + c = 90. Using these equations we can determine the value of b + c: 50 + b + c = 90 b + c = 40 Since b + c = 40, the sum of the discounts for b and c is 0.1(40) =$4, and we know from statement two that the discount for the most expensive item is $10. Thus, the sum of the discounts is 4 + 10 =$14.

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

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1) the average (arithmetic mean) of the regular prices of the 3 items was $30. Sum of three articles is 90. No other info.insufficient (2) the regular price of the most expensive of the 3 items was$50

No info about other two
Insufficient

Combining both
Expensive is 50 other cases can be 20,20 or 30,10
20,20 not possible as we have different values here
So 30,10 is only possibility

We can answer question so sufficient

Give kudos if it helps

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

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annaleroy wrote:
Henry purchased three items during a sale. He received a 20% discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts?

(1) the average (arithmetic mean) of the regular prices of the 3 items was $30. (2) the regular price of the most expensive of the 3 items was$50

Let's say that X is the most expensive item.
and the prices of items purchased are in this order: X>Y>Z
So the actual price of the 3 items: X+Y+Z
Discount he got on item X: 0.2X
Price he paid for the item X: 0.8X

Discount he got on item Y: 0.1Y
Price he paid for the item Y: 0.9Y

Discount he got on item Z: 0.9Z
Price he paid for the item Z: 0.9Z

Total discount he got: 0.2X+0.1Y+0.1Z = 0.2X + 0.1 (Y+Z)

Statement A: the average (arithmetic mean) of the regular prices of the 3 items was $30 $$\frac{X+Y+Z}{3} = 30$$ X+Y+Z = 90 Clearly NOT Sufficient Statement B: the regular price of the most expensive of the 3 items was$50
X = 50
Discount on X: 0.2X = 0.2x50 = $10 No information about Y and Z. Not Sufficient Together: X+Y+Z = 90 X = 50 Y+Z = 40 0.2X =$10
0.1 (Y+Z) = 0.1 x 40 = $4 Total Discount:$10+$4 =$14
Sufficient
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Please award kudos, If this post helped you in someway.  Re: Henry purchased three items during a sale. He received a 20% discount   [#permalink] 24 Oct 2018, 10:49
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