SNAP Number Systems Questions

We know that a, b, c and d are distinct even natural numbers less than 10. Therefore, they must be 2, 4, 6 and 8.
Product of the 4 numbers =$$ 2*4*6*8$$ = $$2*2*2*2*3*2*2*2$$ = $$2^7 * 3$$

Therefore, $$2^7 = 128$$ is the highest power of $$2$$ that will definitely divide the product. Hence, option C is the right answer.

Let the two digit number be 10x and y.
ATQ,
(10y+x) = (100+75)% of (10x+y)
10y+x = 7/4 (10x+y)
10y - 7y/4 = 35x/2 - x
33y/4 = 33x/2
y = 2x ---- (a)
And from the question it says that the difference between the digits of the number is 3 so
y-x = 3 ---(b)
So from eq (a) and (b)
We get, y= 6 and x = 3
So the original number is 36.

We know that the number leaves the same remainder when divided by 2,3,4 and 5.
Therefore, the number should be of the form LCM(2,3,4,5) + k.
LCM of 2,3,4,5 is 60.
The largest multiple of 60 below 10,000 is 9960.
2 can leave a remainder of 0 or 1.
Therefore, the largest possible value of k is 1.
The largest 4 digit number that leaves the same remainder when divided by 2, 3, 4 and 5 is 9960 + 1 = 9961.

Therefore, option D is the right answer.