We have to find out whether x > 0, then is √x > x.M7MBA wrote:If x > 0, is √x > x ?
(1) x does not equal 1
(2) x*√x > x^2
The OA is the option B.
Why is not sufficient the statement (1)? I am confused here. Experts, can you help me?
There are three cases.
Case 1: If 0 < x < 1
Say x = 1/4, then √x > x => √(1/4) ? 1/4 => 1/2 > 1/4. The answer is Yes.
Note that √x is a positive number.
Case 2: If x = 1
√x > x => √1 = 1 => 1 = 1. The answer is No.
Case 3: If x > 1
Say x = 4, then √x > x => √4 ? 4 => 2 < 4. The answer is No.
So, if 0 < x < 1, the answer is Yes, else No.
(1) x does not equal 1.
Insufficient. Case 1 and Case 3 are applicable in this case.
(2) x*√x > x^2
=> x*(x)^(1/2) > x^2 => x^(1+1/2) > x^2 => x^(3/2) > x^2 => 1 > x^2 / x^(3/2) => 1 > x^(2 - 3/2) => 1 > x^(1/2)
Squaring both the sides, we get 1 > x. Only Case 3 is applicable, thus the answer is No. Sufficient.
The correct answer: B
Hope this helps!
-Jay
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