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# Santa is packing 10 boxes into his sleigh. each box weighs either 20

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Intern
Joined: 24 Nov 2018
Posts: 15
Location: India
Santa is packing 10 boxes into his sleigh. each box weighs either 20  [#permalink]

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Updated on: 03 Jan 2019, 07:18
4
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:38) correct 47% (02:27) wrong based on 77 sessions

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Santa is packing 10 boxes into his sleigh. each box weighs either 20 pounds or 30 pounds, and the average weight of all 10 boxes is 27 pounds. Because the sleigh is too heavy, Santa must reduce the average weight of the boxes in the sleigh to exactly 25 pounds by removing some of the 30-pound boxes. How many 30 pound boxes must Santa remove?

A) 1
B) 2
C) 3
D) 4
E) 5

Originally posted by divyadamahe on 03 Jan 2019, 07:11.
Last edited by Bunuel on 03 Jan 2019, 07:18, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Santa is packing 10 boxes into his sleigh. each box weighs either 20  [#permalink]

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03 Jan 2019, 07:17
Please follow rules of posting - refer to point 1 in my signature.

Santa is packing 10 boxes into his sleigh. each box weighs either 20 pounds or 30 pounds, and the average weight of all 10 boxes is 27 pounds. Because the sleigh is too heavy, Santa must reduce the average weight of the boxes in the sleigh to exactly 25 pounds by removing some of the 30-pound boxes. How many 30 pound boxes must Santa remove?

A)1
B)2
C)3
D)4
E)5

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Manager
Joined: 28 Jul 2016
Posts: 246
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
Re: Santa is packing 10 boxes into his sleigh. each box weighs either 20  [#permalink]

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03 Jan 2019, 09:42
current avg weight= 27
using alligation method:
there are 3 -20 pound boxes and 7- 30 pound boxes.
We have to remove 30 pound boxes to make avg as 25
hence
$$(20*3 +30*(7-k))/10-k =25$$

where k is the number of boxes to remove
Solve for k .
Hence D
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Intern
Joined: 24 Dec 2018
Posts: 40
Location: India
Re: Santa is packing 10 boxes into his sleigh. each box weighs either 20  [#permalink]

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03 Jan 2019, 09:48
2
Let # of 30 pound boxes be x. Then # of 20 pound boxes will be 10-x.

Now we are given that average weight of these 10 boxes is 27 pounds. This can be expressed as:
30x+20(10-x)=270
=> 30x+200-20x=270
=> x=7

Thus # of 30 pound boxes is 7 and similarly, # of 20 pound boxes is 10-7=3

We are also given that a few of the 30 pound boxes are being removed so that average weight can be reduced to 25. Let # of boxes removed by a
Thus, 20*3+30(7-a)=25*(10-a)
=> 60+210-30a=250-25a
=> 270-250=30-25a
=> 20=5a
=> a=4

Thus option is D
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Re: Santa is packing 10 boxes into his sleigh. each box weighs either 20  [#permalink]

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01 Feb 2019, 22:26
Santa is packing 10 boxes into his sleigh. each box weighs either 20 pounds or 30 pounds, and the average weight of all 10 boxes is 27 pounds. Because the sleigh is too heavy, Santa must reduce the average weight of the boxes in the sleigh to exactly 25 pounds by removing some of the 30-pound boxes. How many 30 pound boxes must Santa remove?

A) 1
B) 2
C) 3
D) 4
E) 5

I used allegation method here

10 boxes, each box weighs either 20 pounds or 30 pounds

20---------------30
--------27---------
3-----------------7

3:7 is the ratio in which the boxes will be divided into and since they are 10 boxes

3, 20 lbs boxes and 7, 30 lbs boxes will be present

20---------------30
--------25---------
5-----------------5

1:1, is the ratio in which the boxes will be divided into

(i didn't read this part when i had initially solved the question)
Santa

must reduce the average weight of the boxes in the sleigh to exactly 25 pounds

by removing some of the 30-pound boxes.

That meant that the current ratio will be 3:3

Initial boxes
20---------------30
--------27---------
3-----------------7

Current boxes
20-----------30
3-------------3

Reduction of 30 lbs boxes will be 7-3 = 4

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Re: Santa is packing 10 boxes into his sleigh. each box weighs either 20   [#permalink] 01 Feb 2019, 22:26
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