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Box shipment

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Box shipment [#permalink] New post 15 Oct 2008, 13:08
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Last edited by spiridon on 15 Oct 2008, 13:38, edited 1 time in total.
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Re: Box shipment [#permalink] New post 15 Oct 2008, 13:26
(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 :wink:

Last edited by yezz on 15 Oct 2008, 13:50, edited 1 time in total.
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Re: Box shipment [#permalink] New post 15 Oct 2008, 13:34
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 ? :roll:
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Re: Box shipment [#permalink] New post 15 Oct 2008, 13:38
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 :(
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Re: Box shipment [#permalink] New post 15 Oct 2008, 13:39
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
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Re: Box shipment [#permalink] New post 15 Oct 2008, 13:55
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?
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Re: Box shipment [#permalink] New post 15 Oct 2008, 14:01
OA is 20

and i got tricked and selected 6 as well!
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Re: Box shipment [#permalink] New post 15 Oct 2008, 14:40
How long did it take for you guys to do this problem? 5+ minutes for me
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Re: Box shipment [#permalink] New post 15 Oct 2008, 14:52
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
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Re: Box shipment [#permalink] New post 16 Oct 2008, 05:10
Its took me over 5 mins, as you can see I was confused - posted 2 answers.

Good question.
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Re: Box shipment [#permalink] New post 16 Oct 2008, 05:39
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.
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Re: Box shipment [#permalink] New post 16 Oct 2008, 06:18
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.
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Re: Box shipment [#permalink] New post 16 Oct 2008, 08:46
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 ? :roll:


So the answer was 20 afterall :)
spiridon: I didn't see 20 as part of the initial list, did you change it later ? :roll:
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Re: Box shipment [#permalink] New post 16 Oct 2008, 09:19
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 ? :roll:


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


yeah made a typo sorrry
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Re: Box shipment [#permalink] New post 16 Oct 2008, 09:33
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
Re: Box shipment   [#permalink] 16 Oct 2008, 09:33
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