If 0

Question

If  0 < √x ≤ \frac{1}{2} , which of the following cannot represent x?

(A)  \frac{1}{2}

(B)  \frac{1}{4}

(C)  \frac{1}{9}

(D)  \frac{1}{16}

(E)  \frac{1}{25}

JerryAtDreamScore · Answer

Breaking Down the Info:

We may square all sides of the inequality to find  0 < x ≤ \frac{1}{4} .

Hence we know x cannot be greater than 0.25 and we can choose A.

Answer: A

GMATinsight · Answer

0 < √x ≤ \frac{1}{2}

Squaring both sides, We get

0 < x ≤ \frac{1}{4}

(A)  \frac{1}{2}   NOT POSSIBLE
 
(B)  \frac{1}{4}  Possible

(C)  \frac{1}{9}  Possible

(D)  \frac{1}{16}  Possible

(E)  \frac{1}{25}  Possible

Answer: Option A

PyjamaScientist · Answer

Thank for the solution. And though I got it right.
I have a small query. Does squaring both sides of an "Inequality" have any effect on the sign of inequality?
We do not cross multiply in inequalities if we do not know the nature of "x" as it can reverse the sign. Is there anything of the same sort with respect to our inequalities as well?

bumpbot · Answer

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If 0 < √x ≤ 1/2, which of the following cannot represent x?

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