Question

If the number 2484X36Y is divisible by 36, find the minimum value of X-Y.
a) 0 b) 1 c) 2 d) -7

Answer 1

Answer:

Option A is correct

Step-by-step explanation:

Given : 2484X36Y is divisible by 36

36 = 3 × 3 × 4

Since, 3 is a factor of 36 so 2484X36Y will also be divisible by 3 and any number is divisible by 3 if and only if sum of its digits is divisible by 3

So, 2 + 4 + 8 + 4 + X + 3 + 6 + Y = 27 + X + Y

⇒ For minimum value : 27 + X + Y = 27 because 27  is itself divisible by 3.

⇒ X + Y = 0.........(1)

Now, since 4 is also a factor of 36. So, 2484X36Y will also be divisible by 4 and any number is divisible by 4 if its last two digits are divisible by 4.

⇒ 6Y is divisible by 4.

So, for minimum value only possibility for Y is Y = 0 because 60 is only multiple of 4.

So, From equation (1),  X = 0

Hence, minimum value of X - Y is 0

So, Option A is correct

Answer 2

The minimum value of X-Y = -7(d)