December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. December 16, 2018 December 16, 2018 03:00 PM EST 04:00 PM EST Strategies and techniques for approaching featured GMAT topics
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 15 Oct 2014
Posts: 5

Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
Updated on: 08 Mar 2015, 12:22
Question Stats:
71% (00:57) correct 29% (00:50) wrong based on 673 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by annaleroy on 08 Mar 2015, 12:21.
Last edited by Bunuel on 08 Mar 2015, 12:22, edited 1 time in total.
Renamed the topic and edited the question.




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13095
Location: United States (CA)

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
08 Mar 2015, 16:18
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: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****




Math Expert
Joined: 02 Aug 2009
Posts: 7108

Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
08 Mar 2015, 18:02
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 9050=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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 07 Feb 2015
Posts: 46

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
08 Mar 2015, 23:52
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 . INSUFFICIENTStatement two : price of max. one = 50 so discount one it = 20 but we dont know about the other two so INSUFFICIENTcombining we get price of other two = 9050=40 i.e. discount on them 40x.1=4 C
_________________
Kudos if it helped you in any way



Intern
Joined: 12 Nov 2014
Posts: 18

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
09 Nov 2015, 07:40
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?



Intern
Joined: 03 Oct 2012
Posts: 8
Concentration: Strategy, Finance

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
09 Nov 2015, 09:40
alice7 wrote: 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



Intern
Joined: 08 Feb 2015
Posts: 23

Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
13 Feb 2016, 08:10
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.



Senior Manager
Joined: 08 Jun 2015
Posts: 435
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38
GPA: 3.33

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
10 Jan 2017, 05:15
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
_________________
" The few , the fearless "



Board of Directors
Joined: 17 Jul 2014
Posts: 2618
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
10 Jan 2017, 15:09
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



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 533
Location: India

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
10 Jan 2017, 23:47
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)xSince 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)zNow 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 $50Here 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 : CCrackVerbal Academics Team
_________________
For more info on GMAT and MBA, follow us on @AskCrackVerbal
Register for the Free GMAT Video Training Course : https://crackverbal.com/MBAThroughGMAT2019Registration



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
11 Jan 2017, 06:53
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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 02 Oct 2017
Posts: 728

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
27 Jun 2018, 09:15
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 Posted from my mobile device
_________________
Give kudos if you like the post



Manager
Joined: 24 Sep 2018
Posts: 138

Re: Henry purchased three items during a sale. He received a 20% discount
[#permalink]
Show Tags
24 Oct 2018, 09:49
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
_________________
Please award kudos, If this post helped you in someway.




Re: Henry purchased three items during a sale. He received a 20% discount &nbs
[#permalink]
24 Oct 2018, 09:49






