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# Box shipment

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Senior Manager
Joined: 04 Aug 2008
Posts: 369

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15 Oct 2008, 14:08
1
This post was
BOOKMARKED
4
6
10
20
24

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_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Last edited by spiridon on 15 Oct 2008, 14:38, edited 1 time in total.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1741

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15 Oct 2008, 14:26
(10x+20y)/30 = 18

10x+20y = 540 ie: x+2y =54

10x+20(y-z) /30-z =14

420-14z = 10x+20y -20z

420+ 6z = 10x+20y,ie: 210+3z = 5x+10y, but 5x+10y = 5(x+2y) ie: 5*54 = 270

210+3z = 270

3z = 60 ,z = 20

not sure though

Last edited by yezz on 15 Oct 2008, 14:50, edited 1 time in total.
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown

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15 Oct 2008, 14:34
10x+20y = 30*18
x+y = 30
y = 24, x = 6

To find the new 20lb boxes
60+20z = (z+6)14
6z = 84-60 = 24
z = 4

So 20 boxes need to be removed.
Where am I going wrong ?
Director
Joined: 27 Jun 2008
Posts: 523
WE 1: Investment Banking - 6yrs

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15 Oct 2008, 14:38
I dont know if my approach is correct or am I missing something?

> 18 (Old Mean)*30 (#of boxes) = 540
> 14 (New mean)*30 = 420

Difference = 120.

Since you need to reduce the 20p boxes, 120/20 = 6 boxes needs to be removed so that he mean reaches 14?

I'm confused
Senior Manager
Joined: 04 Aug 2008
Posts: 369

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15 Oct 2008, 14:39
pawan203 wrote:
I dont know if my approach is correct or am I missing something?

> 18 (Old Mean)*30 (#of boxes) = 540
> 14 (New mean)*30 = 420

Difference = 120.

Since you need to reduce the 20p boxes, 120/20 = 6 boxes needs to be removed so that he mean reaches 14?

I'm confused

your reducement will bring number of boxes to 30-6=24 and if u divide 420 with 24 u get 17.5 not 14
_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Director
Joined: 27 Jun 2008
Posts: 523
WE 1: Investment Banking - 6yrs

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15 Oct 2008, 14:55
spiridon - thanks, i understand.

> (10x+20y)/30 = 18
> 10x+20y=540.....let this be (a)

z = number of boxes to be removed

> (10x+20(y-z))/30-z = 14
> 10x+20y-20z = 14*(30-z)
> 10x+20y-20z = 420-14z
> 540-420 = 20z-14z
> 120 = 6z

z = 20

I dont know if this is correct

D?
Senior Manager
Joined: 04 Aug 2008
Posts: 369

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15 Oct 2008, 15:01
OA is 20

and i got tricked and selected 6 as well!
_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Retired Moderator
Joined: 18 Jul 2008
Posts: 920

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15 Oct 2008, 15:40
How long did it take for you guys to do this problem? 5+ minutes for me
Senior Manager
Joined: 04 Aug 2008
Posts: 369

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15 Oct 2008, 15:52
very good question

at first it took less then a minute but produced wrong answer

second attempt (knowing the a) still took a while

idk how ppl manage to answer all questions on the gmat
_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Director
Joined: 27 Jun 2008
Posts: 523
WE 1: Investment Banking - 6yrs

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16 Oct 2008, 06:10
Its took me over 5 mins, as you can see I was confused - posted 2 answers.

Good question.
Intern
Joined: 03 Sep 2008
Posts: 22

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16 Oct 2008, 06:39
Here's how to do it quickly.

This is a weighted average of 10 and 20. Since 18 is 2/10 of the total distance from 20, this means we use 8/10*30=24 boxes that are 20lbs and 6 that are 10 lbs. The new weighted average of 14 is closer to 10 than 20 so now we must use more 10lb boxes than 20lb boxes. Answer D is the only answer that makes sense.
Manager
Joined: 12 Feb 2008
Posts: 176

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16 Oct 2008, 07:18
Excellent question.

It took me around 5 min as well. almost gave up, but got it.
20 is the answer as well for me.

Where did you get this question from.

Thanks again.
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown

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16 Oct 2008, 09:46
LiveStronger wrote:
10x+20y = 30*18
x+y = 30
y = 24, x = 6

To find the new 20lb boxes
60+20z = (z+6)14
6z = 84-60 = 24
z = 4

So 20 boxes need to be removed.
Where am I going wrong ?

So the answer was 20 afterall
spiridon: I didn't see 20 as part of the initial list, did you change it later ?
Senior Manager
Joined: 04 Aug 2008
Posts: 369

### Show Tags

16 Oct 2008, 10:19
LiveStronger wrote:
LiveStronger wrote:
10x+20y = 30*18
x+y = 30
y = 24, x = 6

To find the new 20lb boxes
60+20z = (z+6)14
6z = 84-60 = 24
z = 4

So 20 boxes need to be removed.
Where am I going wrong ?

So the answer was 20 afterall
spiridon: I didn't see 20 as part of the initial list, did you change it later ?

_________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Current Student
Joined: 28 Dec 2004
Posts: 3309
Location: New York City
Schools: Wharton'11 HBS'12

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16 Oct 2008, 10:33
spiridon wrote:
4
6
10
20
24

I get 20...

equation is as follows

(10x+20(30-x))/30=18

10x+600-20x=30*18

30*20-10x=30*18
30(20-18)=10x; 30(2)=10x; x=6, so there are 24 20-lb boxes

now..

(10*6+20(24-x))/(30-x)=14

60+20*24-20x=14(30-x)

30*2-30*14+24*20=6x

-30(12)+12(2*20)=6x; 12(-30+40)=6x; 12(10)=6x; x=2*10 or 20...

20 boxes need to be moved

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Box shipment   [#permalink] 16 Oct 2008, 10:33
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# Box shipment

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