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Henry purchased three items during a sale. He received a 20% discount

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annaleroy
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Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   Updated on: 08 Mar 2015, 13:22
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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
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C

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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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   08 Mar 2015, 17:18
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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

So, we know that that $50 item gets the 20% discount and the other two items (that add up to $40) each get 10%. The discount will be $50(20%) + $40(10%) = $10 + $4 = $14.
Combined, SUFFICIENT

Final Answer:
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C


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Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   08 Mar 2015, 19:02
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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


Hi annaleroy,

what the question asks us is the total amount of three discounts. we are given value of discount in %, so any statement which can help us in deducting the numerical value of three items or three discounts will be sufficient....
1) statement one tells us that the average of three number is 30.... not sufficient as the values can be anything 40,30,20...40,25,25....30,30,30.. and so on and each will have different amount of discount....
2) it gives the cost of most expensive item as 50... insufficient as we donot know anything about other two values...

combined, we have a mean 30, which gives us total amount as 90.. and one value as 50, which gives us sum of other two values as 90-50=40....
although we donot know the other two values separately, the combined value of 40 is sufficient as the % of discount is same for the two values

ans C
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   09 Mar 2015, 00:52
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Statement one : mean = 30 thus, total sum of three = 90 but since we dnt know the breakdown of the prices we cat calculate the discount .INSUFFICIENT
Statement two : price of max. one = 50 so discount one it = 20 but we dont know about the other two so INSUFFICIENT
combining we get price of other two = 90-50=40 i.e. discount on them 40x.1=4
C
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   09 Nov 2015, 08:40
Hi Guys,
I tried solving in this way and I got E.
Let original cost of three items to be a1,a2,a3.
New discounted prices are: a1n,a2n,a3n
Given information:
a3n: 0.8a3 where a3 is highest
a1 : 0.9a1
a2: 0.9a2
amount of three discount?

1) a1+a2+a3 = 90 or 0.8a3+0.9a1+0.9a2 = 90 --- not sufficent
2) a3 = 50 then a3n = 40 and a1,a2 not provided so not sufficent


COmbining 1 and 2, we are still missing a1, and a2....then why the answer is C?
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   09 Nov 2015, 10:40
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Hi Guys,
I tried solving in this way and I got E.
Let original cost of three items to be a1,a2,a3.
New discounted prices are: a1n,a2n,a3n
Given information:
a3n: 0.8a3 where a3 is highest
a1 : 0.9a1
a2: 0.9a2
amount of three discount?

1) a1+a2+a3 = 90 or 0.8a3+0.9a1+0.9a2 = 90 --- not sufficent
2) a3 = 50 then a3n = 40 and a1,a2 not provided so not sufficent


COmbining 1 and 2, we are still missing a1, and a2....then why the answer is C?


Hi,

Combining 1 and 2, you have the following:
a3 = 50 => a3n = 40. Therefore discount on a3 = 10
a1+ a2 + a3 = 90 and a3 = 50. Therefore, a1+a2 = 40. As there is 10% discount applied on both a1 and a2, same discount will be applicable on the sum of a1 and a2 i.e. a1n + a2n = 36. Therefore discount on a1 and a2 together = 4

Based on the above we can work out the total discount applied, which is 14.

Hope this helps.

Aadi
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Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   13 Feb 2016, 09:10
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



question can be described as Total price: 0.8A + 0.9(B+C).
Need to know A and (B+C) so we can get 0.2A and 0.1(B+C),
From (1) we can get A + B + C but we need A and (B+C) separately. Insufficient.
From (2) we get A. Insufficient.
(1) & (2) give A and (B+C) separately hence sufficient.

Kudos if this helps.
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   10 Jan 2017, 06:15
Option C.

Let the prices be a,b,&c in increasing order. We need to find out 0.1(a+b)+0.2c

First statement - gives a+b+c = 90 - NS
Second statement - c=50 again NS
Combine the two , a+b=40 , c=50. Hence sufficient.
Therefore the answer must be C
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   10 Jan 2017, 16:09
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


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
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   11 Jan 2017, 00:47
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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

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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   11 Jan 2017, 07:53
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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


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.

Answer: C
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   27 Jun 2018, 10:15
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
C is answer

Give kudos if it helps

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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   24 Oct 2018, 10:49
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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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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   31 Oct 2019, 12:15
We have 3 items, a, b and c:
Question: 1/10*(a+b) + 1/5(c) = ?

1) a+b+c /3 = 30
a+b+c = 90
Cannot determine individual cost, not sufficient

2) c = 50, we know c's discount is 10, no information about a,b, not sufficient

Together:
We know c=50, discount is 10
a+b+50 = 90
a+b = 40
40 * 1/10 = 4, sufficient
(note: it doesn't matter how the $40 is divided between a and b, you can test easily to see taking numbers like 10,30 and 20,20 (both give 4)
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   08 Oct 2020, 09:51
Let the prices in ascending order of the three items be A (least expensive), B (middle priced), C (most expensive)

We are asked to determine the value of the following quantity:

0.1A + 0.1B + 0.2C ..............(X)

(1) the average (arithmetic mean) of the regular prices of the 3 items was $30.

This tells us that A + B + C = 90. From this alone, we cannot determine the value of the quantity in (X). INSUFFICIENT


(2) the regular price of the most expensive of the 3 items was $50

This only tells us that C = 50. From this alone, we cannot determine the value of the quantity in (X). INSUFFICIENT

Statements (1) and (2) together:

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

Combining the two statements, we get:

A + B + 50 = 90

or, A + B = 40

Therefore, the value of the quantity in (X) is 0.1(40) + 0.2(50) = 14. SUFFICIENT

ANSWER: (C)
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   17 Aug 2022, 06:31
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



I solved it this way:

Lets take a > b > c
We need to find D = a/5 + b/10 + c/10

1] a+b+c = 90
divide by 10 --> 1/10 ( a+b+c) = 9 ...........lower limit of D

divide by 5 --> 1/5 ( a+b+c) = 18...............upper limit of D

Cant find D
insuff

2] a=50 so a/5 = 10
cant find D
insuff

Together]
1/10 ( b+c) = 4
1/5 ( 50) = 10
D = 14
suff!
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink] New post   17 Aug 2023, 13:46
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Re: Henry purchased three items during a sale. He received a 20% discount [#permalink]
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