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

by nataras » Sat Jul 05, 2014 9:54 am
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. 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.

OA: C[/spoiler]

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by GMATGuruNY » Sat Jul 05, 2014 6:30 pm
nataras 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. 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:
A = the regular price of the most expensive item
B = the regular price of the second most expensive item
C = the regular price of the third most expensive item.
Then:
Sum of the 3 discounts = (20% of A) + (10% of B) + (10% of C).

Statement 1: The average (arithmetic mean) of the regular prices of the 3 items was $30.
Thus:
A+B+C = (number of prices)Iaverage price) = 3*30 = 90.

Case 1: A=70, B=20, C=10
In this case, the sum of the 3 discounts = 14 + 2 + 1 = 17.
Case 2: A=40, B=30, C=20,
In this case, the sum of the 3 discounts = 8 + 3 + 2 = 13.

Since different total discounts are possible, INSUFFICIENT.

Statement 2: The regular price of the most expensive of the 3 items was $50.
Case 3: A=50, B=40, C=30
In this case, the sum of the 3 discounts = 10 + 4 + 3 = 17.
Case 4: A=50, B=20, C=10
In this case, the sum of the 3 discounts = 10 + 2 + 1 = 13.

Since different total discounts are possible, INSUFFICIENT.

Statements combined:
Statement 1: A+B+C = 90.
Statement 2: A=50.
Thus, B+C = 40.
Sum of the 3 discounts = (20% of A) + (10% of B+C) = 10 + 4 = 14.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Sat Jul 05, 2014 6:58 pm, edited 1 time in total.
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by [email protected] » Sat Jul 05, 2014 6:39 pm
Hi nataras,

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

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by GMATinsight » Mon Jul 21, 2014 9:53 am
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. 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,
A = Price of Most expensive item
B = Price of Medium expensive item
C = Price of Least expensive item.

Total Discount = 0.2 A + 0.1 B + 0.1 C =

Question: Total Discount($) = 0.2A + 0.1(B+C) = ?

Statement 1) A + B + C = 3x30 = $90
Individually A and B+C are unknown therefore INSUFFICIENT


Statement 2) A = $50
B+C is unknown therefore INSUFFICIENT

Combining the Two statements
A + B + C = $90 and A = 50 i.e. B+C = 40

Therefore, 0.2A + 0.1(B+C) = 0.2x50 + 0.1x40 = $9
SUFFICIENT

Answer: Option C
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by gmatstudent2017 » Sun Sep 03, 2017 5:35 am
Hi GMAT Guru, and Rich,

I had actually done all of the work you two listed out, but ended up choosing answer choice E instead of answer choice C because of the fact that the discount was "on the regular price of EACH of the other two items." Therefore, I thought you would need to know the cost of the other two items because even though you know that most expensive item is $50, the other two items can be any price that adds up to the remaining $40. For example, the two prices can be $20 and $20, $15 and $25, $1 and $39 etc. During the exam I didn't think to work through the numbers, but after the exam I realized that any combination of numbers that add up to $40 will still result in $4 when you take 10% of each and add those values together. I guess my question is how can you tell that 10% of the sum of both of the numbers would equal to 10% of each of the individual values added together? In other words 10% of 40 is 4, so how can you tell that when you take 10% of any 2 numbers that add up to 40 the final result will be 4?
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by DavidG@VeritasPrep » Sun Sep 03, 2017 10:04 am
gmatstudent2017 wrote:Hi GMAT Guru, and Rich,

I had actually done all of the work you two listed out, but ended up choosing answer choice E instead of answer choice C because of the fact that the discount was "on the regular price of EACH of the other two items." Therefore, I thought you would need to know the cost of the other two items because even though you know that most expensive item is $50, the other two items can be any price that adds up to the remaining $40. For example, the two prices can be $20 and $20, $15 and $25, $1 and $39 etc. During the exam I didn't think to work through the numbers, but after the exam I realized that any combination of numbers that add up to $40 will still result in $4 when you take 10% of each and add those values together. I guess my question is how can you tell that 10% of the sum of both of the numbers would equal to 10% of each of the individual values added together? In other words 10% of 40 is 4, so how can you tell that when you take 10% of any 2 numbers that add up to 40 the final result will be 4?
It's really just an application of the distributive property of multiplication. You're looking for the sum of 10% of one value and 10% of another value. Algebraically, you want .10x + .10y. This is the same as .10(x + y,) so having the sum of the two values is just as good as having the values individually.

But generally speaking, if you think that something is obviously insufficient, take the extra 15 seconds to prove it. In other words, if you'd picked two sets of numbers that yielded different results, you'd know for certain that a given statement or statements were not sufficient and you wouldn't have to worry about a hidden surprise. But if you pick two sets of numbers and you're surprised to find that they yield the same result, that's a good indication that you may, in fact, have a bit more information than you'd initially suspected.
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by Scott@TargetTestPrep » Mon Sep 11, 2017 10:23 am
nataras 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. 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.

OA: C[/spoiler]

We can let a = the least expensive item, b = the next most expensive item, and c = the most expensive item. We need to determine:

0.1a + 0.1b + 0.2c = ?

0.1(a + b) + 0.2c = ?

Statement One Alone:

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

We can create the following equation:

(a + b + c)/3 = 30

a + b + c = 90

a + b = 90 - c

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.

We see that c = 50; however, we cannot answer the question.

Statements One and Two Together:

From statements one and two, we have:

a + b = 90 - c and c = 50

Thus, a + b = 40.

So, the sum of all the discounts is:

0.1(40) + 0.2(50) = 4 + 10 = 14 dollars

Answer: C

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