In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is same as that on the right side of :: ?

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

X : 729 :: 13 : Y

Given: ​X : 729 :: 13 : Y​

​​Sol.

729 is the cube of 9. (9 × 9 × 9 = 729)
So, X = 9.

Now, find Y for 13:
13 × 13 × 13 = 2197
So, Y = 2197.

Logic: (1st number)³ = 2nd number

X = 9 is correct (because 9³ = 729),

but 13³ is not 1320, it should be 2197.

So, (a) is wrong.

9³ = 729 

13³ = 2197 

So, (b) is correct.

27³ = 19683, not 729 

Also, 13³ is not 1440.

So, (c) is wrong.

11³ = 1331, not 729 

13³ is not 2132 either.

So, (d) is wrong.

Thus, option (b) is correct.​​