Question

If a, b, c and d are four odd perfect cube numbers,

then which of the following is always a factor of

    2 33 33 ab cd   ?

(1) 6

(2) 8

(3) 3

(4) 9

Answer 1

It is given that a, b,c,d are four odd perfect cube  numbers.

As the unit digit of 2 33 33 ab cd

will always be odd.

Take any four perfect odd cube numbers and replace these numbers by a, b,c,d .

Now , 6=incorrect, because unit digit is odd,

          8= incorrect, because unit digit is odd,

          3= correct, because as you will see sum of the digits is always divisible by 3.

9 = Incorrect , If the number is divisible by 3 , it may or may not be divisible by 9.

Out of all the options given (3) 3 is always factor of 2 33 33 ab cd .

Answer 2

Thank you for asking this question. Here is your answer:

a = 1

b = 8

c = 125

d = 343

These are the four odd perfect cube numbers

∛a=∛1=1,∛b=∛8=2,∛c=∛125=5  and ∛d=∛343=7  

(∛a+∛b)^2 (∛c  ∛d) will be 192, 360, 512, 576 and 600

(192, 360, 512, 576, 600) = 8

So this means that 8 will always be the factor of (∛a+∛b)^2 (∛c+∛d)

If there is any confusion please leave a comment below.