Which of The Following is a Perfect Cube? GMAT Problem Solving

Question: Which of the following is a perfect cube?

1. 39316
2. 27006
3. 46658
4. 32768
5. 64012

“Which of the following is a perfect cube?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2021”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

There is only one approach to solve the problem.

Whenever a question is asked on square roots in GMAT, there is a bigger chance of it testing the units digit concept. However the cuberoot generally can have any units digit.
We will start by checking the units digit.
Since all numbers are even, we will now see the possible units digit of even numbers (2, 4, 8 etc)
(A) numbers ending in 0 - 0*0*0=0
(B) numbers ending in 2 - 2*2*2=8
(A) numbers ending in 4 -4*4*4=4
(A) numbers ending in 6 - 6*6*6=6
(A) numbers ending in 8 - 8*8*8=2
We can see from the above that all the digits are possible.
Now, the next step would be to test the answers, or proximity to any known cube. We will be taking all the options provided and test them one by one.
The smallest number in choices is 27006~27000 = \(30^3\)
The largest number in choices is 64012~64000 = \(40^3\)
Now, we are left with
(A) 39316...ending with 6 means ONLY possibility of 36
If we check for \(36^3\)= 46656
Hence, the answer is NO
(B) 27006... This can be discarded based on (A) or proximity to \(30^3\)
(C) 46658...ending with 8 means ONLY possibility of 32
Let us check for \(32^3\)= 32768
Again the answer becomes NO
(D) 32768...Yes as \(32^3\)= 32768
(E) 64012...This can be discarded due to proximity to \(40^3\)

Correct Answer: D

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