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If x < y, is x^2 < y^2 ?

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If x < y, is x^2 < y^2 ?  [#permalink]

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New post 24 Feb 2014, 00:59
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67% (01:01) correct 33% (00:55) wrong based on 212 sessions

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Re: If x < y, is x^2 < y^2 ?  [#permalink]

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New post 24 Feb 2014, 01:06
If x < y, is x^2 < y^2 ?

(1) y > 0 --> y is positive but we don't know the sign of x. If x=0 and y=1, then x^2 < y^2 but if x=-100 and y=1, then x^2 > y^2. Not sufficient.

(2) x > 0 --> 0 < x < y. Now, since both sides of the inequality x < y are non-negative, then we can safely square: x^2 < y^2. Sufficient.

Answer: B.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

Hand-picked 50 GMAT Data Sufficiency Questions on Inequalities with Solutions: 50-gmat-data-sufficiency-questions-on-inequalities-167841.html

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If x < y, is x^2 < y^2 ?  [#permalink]

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New post 23 Jul 2015, 18:58
:shock:, Si x < y, la condición necesaria para que x^2 < y^2 es: x > 0. YA QUE SI X>0, AL SER Y>X, AMBOS SON POSITIVOS
Luego Respuesta correcta B.

En 1) se afirma que y>0, si esto ocurre, y es positivo, y deja a x en un entorno por una parte positivo y por otra parte negativo, pudiendo estar tan alejado del cero como queramos (en los negativos), esta afirmación produce ambiguedad, para algun valor de x se cumplira x^2<y^2, para otro algún valor de x se cumplira x^2>y^2. AMBIGUEDAD. No es suficiente.

:roll: Es interesante considerar que una afirmación del tipo y < 0, es suficiente, ya que no produce ambiguedad, e indica inobjetablemente que x^2 < y^2, no se cumple.

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Re: If x < y, is x^2 < y^2 ?  [#permalink]

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New post 25 Jul 2015, 16:08
Thanks Bunuel. Kept is simple while solving. In first case, I assumed Y = 1 in which case option 1 is ruled out as x^2 can be greater or lesser than y^2. in second case also assume x=1 in which case y would always be positive and data would be sufficient. To be on the safe side tried with x = 0.5 also in which case too option 2 was sufficient.
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Re: If x < y, is x^2 < y^2 ?  [#permalink]

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