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12 May 2017, 05:17
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45% (medium)

Question Stats:

64% (01:38) correct 36% (02:25) wrong based on 75 sessions

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The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item? A.$1.01
B. $1.06 C.$1.10
D. $1.12 E.$1.18

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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink] ### Show Tags 12 May 2017, 05:23 Bunuel wrote: The original price of an item is$1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01 B.$1.06
C. $1.10 D.$1.12
E. $1.18 Total Price Lenny paid = 4*1.40 + 5* 1.4 *0.8 + 5*1.4*0.6 = 1.4*(4+4+3) =1.4*11 Average price paid per item = 1.4 *11/ 14 =$1.10

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16 May 2017, 06:06
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item? A.$1.01
B. $1.06 C.$1.10
D. $1.12 E.$1.18

Original price = 1.40
4 items bought at full price = 4 x 1.40 = 5.60
5 items bought at a 20% discount = 5 x ( 80% of 1.40) = 5 x ($$\frac{80}{100}$$ x 1.40) = 5.60
5 items bought at a 40% discount = 5 x (60% of 1.40) = 5 x ($$\frac{60}{100}$$ x 1.40) = 4.20

Total number of items = 5+5+4 = 14
Total price of 14 items = 5.60 + 5.60 + 4.20 = 15.40
Average price = $$\frac{15.40}{14}$$ = $1.10 Answer C.... _________________ Kindly press "+1 Kudos" to appreciate CEO Joined: 12 Sep 2015 Posts: 2864 Location: Canada Re: The original price of an item is$1.40. Lenny bought 4 items at full  [#permalink]

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16 May 2017, 06:45
Top Contributor
Bunuel wrote:
The original price of an item is $1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item? A.$1.01
B. $1.06 C.$1.10
D. $1.12 E.$1.18

We can also apply the weighted averages formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

So, average price paid = (proportion of items bought at full price)(full price) + (proportion of items bought at 20% off)(price at 20% off) + (proportion of items bought at 40% off)(price at 40% off)

The TOTAL number of purchases = 4 + 5 + 5 = 14
Full price = $1.40 Price with 20% discount = (0.8)($1.40)
Price with 40% discount = (0.6)($1.40) So, average price paid = (4/14)($1.40) + (5/14) (0.8)($1.40) + (5/14) (0.6)($1.40)

IMPORTANT: Notice that, when $1.40 is multiplied by each fraction with 14 in the denominator, the product is a nice number to work with. For example, (4/14)($1.40) = (4)($0.10) =$0.40
And (5/14) (0.8)($1.40) = (5)(0.8)($0.10) = $0.40 And (5/14) (0.6)($1.40) = (5)(0.6)($0.10) =$0.30

So, we get: average price paid = $0.40 +$0.40 + $0.30 =$1.10

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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink] ### Show Tags 16 May 2017, 07:47 Bunuel wrote: The original price of an item is$1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01 B.$1.06
C. $1.10 D.$1.12
E. $1.18 Cost price of the items is = (1.40*4) + (5*80%*1.40) + (5*60%*1.40) Cost price of the items is = 5.6 + 5.6 + 4.2 Cost price of the items is = 15.4 He bought a total of 14 items, so average price is 1.10 Thus, answer must be (C)$1.10
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Re: The original price of an item is $1.40. Lenny bought 4 items at full [#permalink] ### Show Tags 19 May 2017, 06:17 Bunuel wrote: The original price of an item is$1.40. Lenny bought 4 items at full price, 5 of the same item at a 20% discount, and another 5 of the same item at a 40% discount. What is the average price he paid per item?

A. $1.01 B.$1.06
C. $1.10 D.$1.12
E. $1.18 Since the original price of an item is 1.40, the price with a 20% discount is 0.8 x 1.40 =$1.12 and the price with a 40% discount is 0.6 x 1.40 = $0.84. Since 4 items were purchased at full price, the total spent on those items was 1.4 x 4 =$5.60. Since 5 items were purchased at a 20% discount, the total spent on those items was 5 x 1.12 = $5.60. Finally, since 5 items were purchased at a 40% discount, the total spent on those items was 5 x 0.84 =$4.20.

The average price per item was:

(5.6 + 5.6 + 4.2)/14 = 15.4/14 = $1.10. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: The original price of an item is$1.40. Lenny bought 4 items at full &nbs [#permalink] 19 May 2017, 06:17
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