Latest GRE Aptitude Question SOLUTION: Which of the following inequalities have at least one positive solution and at least one negative solution? Indicate all such inequalities. (A) 5/3 x < x (B) x^3 < x (C) x

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(#M40151659) GRE Numerical Ability question Inequalities Keep an EYE

Which of the following inequalities have at least one positive solution and at least one negative solution? Indicate all such inequalities.
(A) 5/3 x < x
(B) x^3 < x
(C) x - 6 < x – 7

Asked In GRE Aashu (9 years ago)

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Priya  (7 years ago)

Let us consider the inequality symbol as a normal '='(equal to) but if we multiply/Divide by '-'(minus) both sides then invert the inequality symbol.
First step, grab all values and variables to left hand side.
Next check whether it is +ve or -Ve or both.
(A) (5X/3) < X
(5X/3)-X < 0
X[(5/3)-1]if x^2-1 < 0, then x^2 < 0+1 => x^2 < 1. Since x is always squared, it is always +ve.
So this equation has both +ve and -ve solution for X.

(C) x-6 < x-7
x-6-x-7 < 0
-6-7

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