The inside of a rectangular carton is 48 centimeters long, 3

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Feb 15, 2019 6:15 pm

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The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?

(1) Each of the cans has a radius of 4 centimeters.
(2) Six of the cans fit exactly along the length of the carton.

OA D

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Fri Feb 15, 2019 6:15 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sat Feb 16, 2019 4:46 am

BTGmoderatorDC wrote:

The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?

(1) Each of the cans has a radius of 4 centimeters.
(2) Six of the cans fit exactly along the length of the carton.

OA D

Source: Official Guide

Let's take each statement one by one.

(1) Each of the cans has a radius of 4 centimeters.

Thus, the diameter of each can = 8 cm and 48/8 = 6 cans can fit in a row; similarly, 32/8 = 4 cans can fit in a column.

Thus, k = 6*4 = 24. Sufficient.

(2) Six of the cans fit exactly along the length of the carton.

=> Diameter of each can = 48/6 = 8 cm.

Above is the same information as we have in Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Feb 23, 2019 5:42 am

If the cans are 15 cm high, what is the value of K?
Statement 1
Each of the cars has a radius of 4 cm
This means Diameter=2r = 2*4 = 8 cm
Therefore, along the 48 cm length of the carton
Diameter = 48/=6 cans can be placed thus K=6*4=24
thus statement 1 is SUFFICIENT.

Statement 2
Six of the cans fit exactly along the length of the carton
Diameter= 48/6=8
along the 48 cm length of the carton 6 can be placed thus 6*4=24
Statement 2 is also SUFFICIENT.

$$Option\ D\ is\ correct$$

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