Does at least one root of the equation x^2 - 2x - 35 = 0 lie between

x^2 - 2x - 35 = 0
(x-7)(x+5) = 0
x = 7 or -5

Statement 1:ab<0
This statement tells us that one of a or b is negative and the other is positive.
So if a = -1 and b is 8, then one of the roots is in between a and b
But if a is -1 and b is 2, then none of the roots is in between a and b.
This statement is not sufficient.

Statement 2: a+b>10
So if a = 3 and b is 8, then one of the roots is in between a and b
But if a is 11 and b is 22, then none of the roots is in between a and b.
This statement is not sufficient.

Combining the two statements, we know one of a or b is positive and the other is negative.

So if a is negative, the maximum value a can take is -1,
so applying that to a+b>10, gives b >11, so 7 is in between a and b.

As b is positive, the minimum value b can take is 1.
so applying that to -a+b>10, gives a < -9, so 7 is in between a and b.

Combining both statements is sufficient.

Answer is C