What is the greatest number of blocks 8 centimeters by 6 centimeters

Question

What is the greatest number of blocks 8 centimeters by 6 centimeters by 9 centimeters that will fit into a storage space that is 60 centimeters by 72 centimeters by 96 centimeters?

A. 60
B. 840
C. 896
D. 960
E. 1,080

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DavidTutorexamPAL · Accepted Answer

To compare the volume of the blocks with that of the storage space, we'll see how many can fit into each of the sides.
This is a Logical approach.

volume of space = 60 * 72 * 96 = 6 * 10 * 8 * 9 * 96 = 6*8*9 * 960 = volume of one block * 960.
So at most 960 blocks fit. Let's see if this actually works.

The 60 cm side can fit 10 blocks on their 6cm side.
The 72cm side can fit 8 blocks on their 9cm side.
The 96cm side can fit 12 blocks on their 8cm side.

Since 10*8*12 = 960, this works!

(D) is our answer.

Archit3110 · Answer

simple <20 sec
60*72*96/ 8*6*9
IMO D
960

jplaca · Answer

It's important to be aware that both 72 and 96 are divisible by 2 or more of the given numbers. Therefore, it's best to create a table and understand which divisors (6, 8, 9) go into which number (60, 72, 96).

Once you draw a table, it's easy to select the greatest numbers that satisfy the question: 
96 / 8 = 12
60 / 10 = 10
72 / 9 = 8

12 * 10 * 8 = 960

ScottTargetTestPrep · Answer

The greatest number of blocks can be fit into the storage space is:

60/6 x 96/8 x 72/9 = 10 x 12 x 8 = 960

Answer: D

Nipungupta9081 · Answer

Surface Volume of storage space / Surface area of block.

60*72*96/ 8*6*9
IMO D
960

MHIKER · Answer

The greatest number of blocks is:

\frac{60}{6} * \frac{96}{8} * \frac{72}{9}   = 10 * 12 * 8 = 960

The Answer is D.

Abhishek009 · Answer

\frac{60*72*96}{8*6*9}=960 , Answer must be (D)

pr2299 · Answer

Short question, why is it not possible to use prime factorisation? I tried to split 60*96*72 up into 2^10*3^4*5^1.. But it is not right

I am having a huge mistake here but I cant recognise it

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=jpidksnBdfQ

woohoo921 · Answer

Bunuel 
I thought that there was a rule that you cannot take the volumes of certain objects to see how they fit within the volume of another object? I believe there was a problem in this nature in which it was asking for the number of books that can fit inside a bookshelf, but there were actually limits that the volumes of the individual books did not meet. Thank you for your insights in advance.

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What is the greatest number of blocks 8 centimeters by 6 centimeters

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What is the greatest number of blocks 8 centimeters by 6 centimeters

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