If x 0, is √x x ?

Question

If x > 0, is √x > x ?

(1) x does not equal 1
(2) x*√x > x^2

Kudos for a correct  solution .

shelrod007 · Answer

If x > 0, is √x > x ?

We are given here X is positive , GOLDEN RULE : X can be anything integer or fraction .

Statement 1 : 
(1) x does not equal 1

X= 2

\sqrt{2} > 2  No

X = 3

\sqrt{3} > 3  No

X =  \frac{1}{4}

\sqrt{\frac{1}{4}} > \frac{1}{4}  Yes

i.e  \frac{1}{2} > \frac{1}{4}

Therefore Statement 1 is not sufficient .

Statement 2 :

(2) x*√x > x^2

X =  \frac{1}{4}

\frac{1}{4}*\sqrt{\frac{1}{4}} > \frac{1}{4}^2  Yes

Only fractions satisfy this equation... Now coming back to the question stem the answer would always be a Yes .

Hence the answer is B

romitsn · Answer

Statement 1:  -  x
eq{1}

So if x=4 then  \sqrt{4}  > 4 - Not true
However if X= 0.09,  \sqrt{0.09} =0.3 > 0.09 - True
Not sufficient

Statement 2 
 x\sqrt{x}  >  x^{2} 
Since x> 0, we can divide by x on both sides and get,
 \sqrt{x}  >  x^  - Sufficient.

Thus B.

chetan2u · Answer

ans B.. since x>0, for √x > x , 0 √x.. 1) statement 1 tells us that x is not equal to 1.. insufficient 2) statement 2 tells us x*√x > x^2.. x*√x -x^2>0.. x*(√x- x)>0... as x> 0, √x>x for the equation to be positive.. sufficient

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: B

Explanation:

(1) The answer to the question stem will be "yes" only if x is a fraction between 0 and 1. This statement does not tell us whether this is the case, and is therefore insufficient.

(2) To simplify this inequality, divide each side by x. This gives us sqrt x > x, which guarantees that the answer to the question is "yes." Accordingly, since statement 2 alone is sufficient to answer the question, B is the correct answer.

NOTE: When we divide each side of an inequality by an unknown, we need to know whether that unknown is positive or negative. If it is positive, we don't alter the direction of the inequality. If it is negative, we need to flip the direction of the inequality. If we cannot determine whether it is positive or negative, we cannot divide by that variable.

EMPOWERgmatRichC · Answer

Hi All,

DS question can sometimes be written with "math fat", meaning that with a little bit of work, you can strip away the "fat" and "rewrite" the question to make the entire prompt easier to answer.

Here, we're told that X > 0, so X MUST be positive. We're asked if √x > x. This is a YES/NO question.

If you think about this question, there are SOME values that will give us a YES answer and some answers that will give us a NO answer. IF X is 1 or greater than 1, then the answer will be NO.
If 1 > X > 0, then the answer to the question is YES.

Knowing these Number Properties, we can 'rewrite' the question - it's really asking "is X a positive fraction less than 1?"

Fact 1: X does NOT equal 1.

IF....
X = 1/2, then the answer is YES
X = 2, then the answer is NO
Fact 1 is INSUFFICIENT

Fact 2: x(√x) > x^2

If we square both sides, we end up with...
X^3 > X^4

Given the restrictions, this only occurs when X is a positive fraction less than 1, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

If x > 0, is √x > x ?

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