Data Sufficiency

If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a.

(2) Each of a^2b and ab^2 is divisible by 40

Statement 1: b = a + 60% of a = 160a/100 = 8a/5
As b is a positive integer, a must be divisible by 5.
Say, a = 5k, where k is some positive integer.
Now, ab = a*(8a/5) = (5k)*(8k) = multiple of 40
So, the remainder when ab divided by 40 is 0.
So, statement 1 is sufficient

Statement 2:
If a = 2 and b = 10, a²b = 40 and ab² = 200 are both divisible by 40 but ab = 20 leaves a remainder of 20 when divided by 40
If a = 4 and b = 10, a²b = 160 and ab² = 400 are both divisible by 40 and ab = 40 leaves a remainder of 0 when divided by 40

So, statement 2 is not sufficient

Answer : A

A

I have nothing to add to the statement 2 explanation.

1: b is 60% greater than a. (b = 1.6a)

If a is 1, then b is 1.6 - not an integer.
a = 2 b not an integer
a=3 b not an integer
a=4 b not an integer
a=5 b is an integer = (5*1.6) = 8 5*8 = 40 no remainder when divided by 40.
a=6,7,8,9 b is not an integer.
a=10, b = 16 with 5 and 8 as factors (see a=5), so the remainder is 0 when divided by 40.
When a is a multiple of 5, b is an integer, and ab is divisible by 40 (no remainder).

1 is sufficient.