agarwalva wrote:what is remainder when X is divided by 5

1) X divide by 10 has a remainder of 7
2) x divided by 2 has a remainder of 1

The best way to tackle this problem is to pick numbers

Statement (1) X divided by 10 has a remainder 7
So X could be 17, 27, 37, 47, 57... (notice that this is an evenly spaced set)
So now that we have values for X, let's try to find the remainder if X is divided by 5
17/5 = 5(3) + 2
27/5 = 5(5) + 2
37/5 = 5(7) + 2

See: the remainder is 2, so Statement (1) is sufficient

Statement (2) X divided by 2 has a remainder 1
So could be 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 ... (notice that this is also an evenly spaced set)
So now that we have values for X, let's try to find the remainder if X is divided by 5
7/5 = 5(1) + 2
11/5 = 5(2) + 1
19/5 = 5(3) + 4
21/5 = 5(4) + 1

See how we arrive at different values for the remainder? (2, 1, 4, etc.)

This means that Statement (2) is insufficient.

So the answer is A.

The key takeaway here is with these kinds of problems, it would be best not to be afraid to pick numbers. It works wonders as long as you satisfy the conditions.

All the best!

I think solution provided by mdavidm_531 is right as I calculate but here is one funny solution which is also interesting.
Let's try to solve it in simple way
x is divided by 10 remainder is 7
let it is 7

x is divided by 2 and get 1 as remainder
obviously 7

now x is divided by 5 and we get remainder 2
if x is 7.

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