November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 12 Oct 2008
Posts: 456

Each of the 30 boxes in a certain shipment weighs either 10
[#permalink]
Show Tags
09 Oct 2009, 22:25
Question Stats:
65% (02:36) correct 35% (02:40) wrong based on 863 sessions
HideShow timer Statistics
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed? A. 4 B. 6 C. 10 D. 20 E. 24
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: Boxes
[#permalink]
Show Tags
09 Oct 2009, 23:07
reply2spg wrote: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed? A. 4 B. 6 C. 10 D. 20 E. 24 This is a weighted average question: \(Weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}\). Let \(x\) be number of 10pound boxes > \(\frac{10x + 20*(30x)}{30}=18\) > \(x=6\); We have \(6\) 10pound boxes and \(24\) 20pound boxes. Let \(y\) be number of 20pound boxes that should be removed so that average to become 14 pounds > \(\frac{10*6+20*(24y)}{30y}=14\) > \(y=20\). Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 210

Re: Boxes
[#permalink]
Show Tags
21 Aug 2011, 09:59
total current weight = 30*18 = 540 let's assume that x number of 20lbs boxes will be removed \(\frac{54020x}{30x} = 14\) x = 20 ............. D
_________________
press +1 Kudos to appreciate posts Download Valuable Collection of Percentage Questions (PS/DS)




SVP
Joined: 29 Aug 2007
Posts: 2378

Re: Boxes
[#permalink]
Show Tags
09 Oct 2009, 22:43
reply2spg wrote: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed? A. 4 B. 6 C. 10 D. 20 E. 24 x = 20 lb box: 20x + 10(30x) = 18(30) x = (540  300)/10 x = 24 If k = removed 20 lb box: 20(24k)+ 10(6) = 14(6+24k) 480  20k + 60 = 420  14k 540  420 = 6k 540  420 = 6k k = 120/6 = 20
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 88
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

Re: Boxes
[#permalink]
Show Tags
12 Dec 2010, 23:28
dont you have to reduce the average weight of 30 booxes to 14 pounds?



Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: Boxes
[#permalink]
Show Tags
13 Dec 2010, 01:47



Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 88
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

Re: Boxes
[#permalink]
Show Tags
13 Dec 2010, 03:43
Bunuel wrote: So, if \(y\) is the number of 20pound boxes that should be removed so that average to become 14 pounds > \(\frac{10*6+20*(24y)}{30y}=14\), (note that as we are reducing the # of 20pound boxes (24) by y then the total # of boxes (30) also will be reduced by y> is this implied or an assumption) > \(y=20\).
. See my comment in Red Italics. What if we make an attempt to keep total number of boxes 30 by adding \(y\) 10pound boxes. Does this have to be specifically mentioned in the question?



Director
Joined: 03 Sep 2006
Posts: 793

Re: Boxes
[#permalink]
Show Tags
13 Dec 2010, 04:15
x boxes of 10pounds y boxes of 20pounds x+y = 30
\((10*x+20*y)/30=18\)
\(10x+20y=540\)
Let ? be the number of 20 pound boxes which should be removed in order to get the average weight of 14pounds
\((10*x+20*y20*?)/(30?)=14\)
\((54020*?)= (42014*?)\)
\(? = (120/6) = 20\)



Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: Boxes
[#permalink]
Show Tags
13 Dec 2010, 04:53
aalriy wrote: Bunuel wrote: So, if \(y\) is the number of 20pound boxes that should be removed so that average to become 14 pounds > \(\frac{10*6+20*(24y)}{30y}=14\), (note that as we are reducing the # of 20pound boxes (24) by y then the total # of boxes (30) also will be reduced by y> is this implied or an assumption) > \(y=20\).
. See my comment in Red Italics. What if we make an attempt to keep total number of boxes 30 by adding \(y\) 10pound boxes. Does this have to be specifically mentioned in the question? You should read the stem more carefully: "If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed?" So stem mentions that the reduction in average weight should be made by removing some of the 20pound boxes. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8537
Location: Pune, India

Re: Boxes
[#permalink]
Show Tags
13 Dec 2010, 21:02
reply2spg wrote: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed? A. 4 B. 6 C. 10 D. 20 E. 24 Long question stem. Best approach here would be to analyze one sentence at a time. Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds.If average of 10 and 20 is 18, the ratio of no. of 10 pound boxes: no of 20 pound boxes is 1:4 (If this concept is not clear, check out http://gmatclub.com/forum/toughds105651.html#p828579) So out of 30 boxes, 6 are 10 pound boxes and 24 are 20 pound boxes. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxesNow average of 10 and 20 pound boxes is to be 14. So ratio of no. of 10 pound boxes:no. of 20 pound boxes = 3:2 The number of 10 pound boxes remain the same so we still have 6 of them. To get a ratio of 3:2, the no of 20 pound boxes must be 4. how many 20pound boxes must be removed?There were 24 of these. Now there are only 4. 24  4 = 20 should be removed.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 02 Nov 2009
Posts: 108

Re: Boxes
[#permalink]
Show Tags
10 Feb 2012, 05:35
N1+ N2 = 30
10(N1) + 20(N1) _____________ =18 N1+ N2
 > solve 10(N1) + 20(N2) = 18(N1) + 18(N2)
So n1 =6 n2 = 24
Now N1 will not change ONLY n2 will change so
reduce the average to 14
10(6) + 20(N2) = 14(6) + 14(N2)
N2 =4
So it has to reduce by 20



Intern
Joined: 23 May 2013
Posts: 19
Location: United Kingdom
WE: Project Management (Real Estate)

Re: Each of the 30 boxes in a certain shipment weighs either 10
[#permalink]
Show Tags
29 May 2013, 04:13
This is how I solved X+Y =30 from condition given 10X+20Y = 540 therefore X=6 and Y = 24 Condition 2 X= 6 Y changes by "n" and avg weight of 30n =14 therefore 10*6 + 20(24n)=14( 30n) after solving the above equation we have n=20 Ans is D
_________________
Correct me If I'm wrong !! looking for valuable inputs



Manager
Joined: 24 Nov 2012
Posts: 157
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: Boxes
[#permalink]
Show Tags
31 May 2013, 12:55
MBAhereIcome wrote: total current weight = 30*18 = 540 let's assume that x number of 20lbs boxes will be removed
\(\frac{54020x}{30x} = 14\)
x = 20 ............. D Faster to use this logic
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper!  Rumi
http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprepcom/  This is worth its weight in gold
Economist GMAT Test  730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test  670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test  680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1  770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test  690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test  710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2  740, Q49, V41 Oct 6th, 2013
GMAT  770, Q50, V44, Oct 7th, 2013 My Debrief  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



Manager
Joined: 20 Jun 2012
Posts: 82
Location: United States
Concentration: Finance, Operations

Re: Each of the 30 boxes in a certain shipment weighs either 10
[#permalink]
Show Tags
10 Jun 2013, 08:24
reply2spg wrote: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20pound boxes, how many 20pound boxes must be removed? A. 4 B. 6 C. 10 D. 20 E. 24 Easy question: suppose 10 pound boxes = x 20 pound boxes = (30x) Given in question >> [x*10+(30x)*20]/30=18 => [x*10+(30x)*20] = 540 eq. 1 .. Leave it like this. Now we have to remove some 20 Pound boxeslet 20 pound boxes removed = a new equation will be >> [x*10+(30xa)*20]/(30a)=14 >> x*10+(30x)*20  20a = 14(30a) From eq 1 >> 540  20a = 420 14a solve for a, and you'll get a=20 .. I made it look quite big, but I solved it under 2 minutes using this in first try on such question
_________________
Forget Kudos ... be an altruist



Current Student
Joined: 19 Nov 2014
Posts: 3
Location: United States
Schools: ISB '17, NUS '17, IIMA , IIMB, IIMC , Great Lakes '17, PGPEX '17, XLRI, IIM Indore'17, IIML'17, ISB PGPPro"18 (A)
GPA: 3.88
WE: Project Management (Pharmaceuticals and Biotech)

Re: Each of the 30 boxes in a certain shipment weighs either 10
[#permalink]
Show Tags
19 May 2015, 12:25
My solution is as below:
10x+ (30x)20 = 540 x=6 (no. of 10 pound boxes) hence 24 is no. of 20 pound boxes
If y is the new no. of 20 pound boxes required to make the average 14 then,
(10*6+20y) /(6+y) = 14
y=4
hence the no. of 20 pound boxes to be removed is 244 = 20 boxes



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12863
Location: United States (CA)

Re: Each of the 30 boxes in a certain shipment weighs either 10
[#permalink]
Show Tags
11 Apr 2018, 19:08
Hi All, This question can be solved in a number of different ways  including by TESTing THE ANSWERS. There's a Number Property rule that can actually make that solution a bit faster. We're told that the average weight is 18 pounds, which makes the total weight 540 pounds (18 pounds x 30 boxes = 540 pounds) Since the box weights are 10 or 20 pounds each, you can figure out the number of each rather quickly. If there were 30 20pound boxes, then the total weight would be 600 pounds. Since the total weight is 540 pounds, that means that 6 of the boxes weigh 10 pounds instead of 20 pounds. So, there are: 6 10pound boxes 24 20pound boxes Since we want to remove some number of the 20pound boxes and get an average weight of 14 pounds, we know that the number of 10pound boxes MUST BE greater than the number of 20pound boxes (this is a Weighted Average Number Property). Since we have 6 10pound boxes, we need to remove at least 19 20pound boxes. We can certainly TEST answer D first OR we can note that answer E (24) would eliminate ALL of the 20pound boxes, which would make the average of the remaining boxes 10 pounds, which is too low (and would prove that answer D was correct). 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!*****




Re: Each of the 30 boxes in a certain shipment weighs either 10 &nbs
[#permalink]
11 Apr 2018, 19:08






