VANGALA GYANESHWAR REDDY wrote:Is x^2 <=2x?
statement 1.x>0
statment 2.x<3

answer please?

Question : Is x^2 <=2x ?
Is x^2 - 2x <= 0?
Rephrased Question : Is x(x - 2) <= 0?

Statement 1) x>0

If x>3 then x and (x-2) both will be positive therefore product of them will be positive.
It answers the Question as NO
For 0<x<2, the answer to the question is YES
INSUFFICIENT

Statement 2) x<3
For 2<x<3, the answer to the question is NO
For 0<x<2, the answer to the question is YES
INSUFFICIENT

Combining the statement we end up checking the range that we have checked already in Statement 2 therefore INSUFFICIENT

Answer: Option E

Here is how I would solve this one in less than 25 secs. See Image.

Here's an approach.

Let's start with the prompt first. 2x ≥ x² implies 2x - x² ≥ 0, or x(2 - x) ≥ 0.

If x(2-x) ≥ 0, one of three things will be true:

1: x = 0
2: 2 - x = 0, in which case 2 = x
3: Both x and (2 - x) are positive, in which case 2 > x > 0

So we know that if 2 ≥ x ≥ 0, we'll have 2x ≥ x².

On the other hand, if x > 2 or 0 > x, we'll have x² > 2x.

S1 tells us that x > 0, but this isn't enough: if x = 2.5, x² > 2x, but if x = 2, 2x ≥ x².

S2 tells us that 3 > x, but this isn't enough: we could still have x = 2.5 or x = 2.

S1 + S2 tells us that 3 > x > 0, but we still don't have enough: we could still have x = 2.5 or x = 2.