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# The inside of a rectangular carton is 90 centimeters long, 45 centimet

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Math Expert
Joined: 02 Sep 2009
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The inside of a rectangular carton is 90 centimeters long, 45 centimet  [#permalink]

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14 Sep 2018, 02:03
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Difficulty:

75% (hard)

Question Stats:

40% (02:03) correct 60% (01:52) wrong based on 38 sessions

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The inside of a rectangular carton is 90 centimeters long, 45 centimeters wide, and k centimeters high. The carton is filled to capacity with 200 identical cylindrical cans of fruit that stand upright in rows and columns. If the cans are 10 centimeters high, what is minimum value of k?

(1) The box fits 4 layers of cans.
(2) The radius of each can is 4.5 centimeters.

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Re: The inside of a rectangular carton is 90 centimeters long, 45 centimet  [#permalink]

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15 Sep 2018, 01:43
Excellent question!

1.if box fits 4 layers of cans that means height shud be 4 times height of a can i.e. 40 cms.
Sufficient.
2.radius of can =4.5 dia=9 cm
Therefore in area of carton 90*45 cm.
No. Of cans will be 10*5 i.e on bottom most tier 50 cans can be kept.
For 200 cans, we need 4 layers therefore.

4 times height of can =40 cms.

Sufficient.

Consider giving kudos if this helped !

Posted from my mobile device
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Re: The inside of a rectangular carton is 90 centimeters long, 45 centimet  [#permalink]

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16 Sep 2018, 09:32
Can somebody explain how statement 2 is also sufficient? I thought the answer should be A.
Manager
Joined: 23 Aug 2016
Posts: 108
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GMAT 1: 660 Q49 V31
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Re: The inside of a rectangular carton is 90 centimeters long, 45 centimet  [#permalink]

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16 Sep 2018, 09:47
1
nithinjohn wrote:
Can somebody explain how statement 2 is also sufficient? I thought the answer should be A.

Hi,

Radius of each can=4.5 cm therefore dia=9 cms.
Now, see that the rectangular box has base area as 90 cm X 45 cm therefore i can put(along its breadth i.e. 45 cms) 5 cans and i can put (along its length i.e. 90 cms) 10 cans.

So the number of cans at the base will be 10 X 5= 50 cans.

Now, we need to keep 200 cans.

Therefore, at base we can keep=50 cans, we need=200/50=4 stacks to keep all the cans in the rectangular box.

Hence the Statement 2 is also sufficient.

I hope it was clear
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Thanks and Regards,

Honneeey.

In former years,Used to run for "Likes", nowadays, craving for "Kudos". :D
Intern
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GMAT 1: 650 Q47 V34
GPA: 3
WE: Editorial and Writing (Entertainment and Sports)
Re: The inside of a rectangular carton is 90 centimeters long, 45 centimet  [#permalink]

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16 Sep 2018, 11:09
Ah okay I got it now, makes sense. Thanks for that
Re: The inside of a rectangular carton is 90 centimeters long, 45 centimet   [#permalink] 16 Sep 2018, 11:09
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