It is currently 19 Oct 2017, 04:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Each of the 30 boxes in a certain shipment weighs either 10

Author Message
Manager
Joined: 04 Jan 2008
Posts: 118

Kudos [?]: 104 [0], given: 0

Each of the 30 boxes in a certain shipment weighs either 10 [#permalink]

### Show Tags

06 Sep 2008, 00:28
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (02:17) wrong based on 1 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 20-pound boxes, how many 20-pound boxes must be removed ?

(A) 4
(B) 6
(C) 10
(D) 20
(E) 24

Kudos [?]: 104 [0], given: 0

Director
Joined: 23 Sep 2007
Posts: 782

Kudos [?]: 235 [0], given: 0

### Show Tags

06 Sep 2008, 00:59
dancinggeometry 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 20-pound boxes, how many 20-pound boxes must be removed ?

(A) 4
(B) 6
(C) 10
(D) 20
(E) 24

D

let x = number of 10lbs boxes
let y = number of 20lbs boxes

10x + 20y = 18(x+y)
y/x = 4/1 or 24/6

so 6 10lbs boxes, 24 20lbs boxes

new average = 14
6(10) + y(20) = 14(6 + y)
y = 4

so 24 - 4 = 20

Kudos [?]: 235 [0], given: 0

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 437 [0], given: 1

### Show Tags

06 Sep 2008, 11:46
1st eq is

10 X + 20 Y = 30 X 18

2nd eq is

10 X + 20 (y-k) = (30-k) X 14

use (1) in (2)

540 -20k = 420 -14k

6k= 120 means k =20

Kudos [?]: 437 [0], given: 1

Intern
Joined: 03 Sep 2008
Posts: 22

Kudos [?]: 10 [0], given: 0

### Show Tags

06 Sep 2008, 15:42
As much as possible you want to avoid algebra when doing GMAT problems.

You can think of this as a weighted average problem with 2/10 of the weight on the value 10 and 8/10 on 20 so there must be 6 of the 10 lbs boxes and 24 of the 20 lbs boxes. Since 14 is closer to 10 than 20, after removing the 20 lbs boxes there must be more of the 10 lbs boxes than the 20 lbs boxes. Answer D is the only answer that makes sense.

Kudos [?]: 10 [0], given: 0

Manager
Joined: 04 Jan 2008
Posts: 118

Kudos [?]: 104 [0], given: 0

### Show Tags

06 Sep 2008, 23:29
OA is D. Bin 2 problem.

Kudos [?]: 104 [0], given: 0

Retired Moderator
Joined: 18 Jul 2008
Posts: 960

Kudos [?]: 294 [0], given: 5

### Show Tags

07 Sep 2008, 11:40
I don't quite understand how you get 2/10 of the weight vs 8/10 on the weight.

Can you explain more closely? Thanks.

lsmv479 wrote:
As much as possible you want to avoid algebra when doing GMAT problems.

You can think of this as a weighted average problem with 2/10 of the weight on the value 10 and 8/10 on 20 so there must be 6 of the 10 lbs boxes and 24 of the 20 lbs boxes. Since 14 is closer to 10 than 20, after removing the 20 lbs boxes there must be more of the 10 lbs boxes than the 20 lbs boxes. Answer D is the only answer that makes sense.

Kudos [?]: 294 [0], given: 5

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1060 [1], given: 5

Location: New York

### Show Tags

07 Sep 2008, 13:11
1
KUDOS
dancinggeometry 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 20-pound boxes, how many 20-pound boxes must be removed ?

(A) 4
(B) 6
(C) 10
(D) 20
(E) 24

Fastest way:
Total weight = 30*18=540
say n= no.of 20 lb boxes to be removed

540-20n =14 (30-n) --> n=20

Weighted average method:10 (x/x+y) + 20 (y/x+y) = 18
should be same as

0 (x/x+y) + 10 (y/x+y) = 8 --> 10*y/30 =8
--> y=24
x=6

-- for 14 weighted average
0 (x/x+y)+10 (y/6+y) = 4 --> 10y = 24+6y
--> y=4

twently 20 pound boxes need to be removed.
_________________

Smiling wins more friends than frowning

Kudos [?]: 1060 [1], given: 5

Current Student
Joined: 06 Oct 2008
Posts: 38

Kudos [?]: 2 [0], given: 0

### Show Tags

23 Oct 2008, 21:45
Hey x2suresh,

Your fastest way is so stupidly easy. I love it! thanks!
I can't believe I didn't think of it like that! I did it the long method and solved it in 4 mins (wasn't happy with my time)

Sumi

Kudos [?]: 2 [0], given: 0

VP
Joined: 30 Jun 2008
Posts: 1034

Kudos [?]: 705 [0], given: 1

### Show Tags

23 Oct 2008, 22:34
x2suresh wrote:
dancinggeometry 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 20-pound boxes, how many 20-pound boxes must be removed ?

(A) 4
(B) 6
(C) 10
(D) 20
(E) 24

Weighted average method:10 (x/x+y) + 20 (y/x+y) = 18
should be same as

0 (x/x+y) + 10 (y/x+y) = 8 --> 10*y/30 =8
--> y=24
x=6

-- for 14 weighted average
0 (x/x+y)+10 (y/6+y) = 4 --> 10y = 24+6y
--> y=4

twently 20 pound boxes need to be removed.

Can someone explain the parts in red ??
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 705 [0], given: 1

Re: Zumit PS 002   [#permalink] 23 Oct 2008, 22:34
Display posts from previous: Sort by