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24 Feb 2014, 01:59
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:16) correct
28%
(01:17)
wrong
based on 1023
sessions
History
Date
Time
Result
Not Attempted Yet
24 Feb 2014, 02:06
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APPROACH 1:
If x < y, is x^2 < y^2 ?
(1) y > 0
We are given that y is positive but we don't know the sign of x. If x = 0 and y = 1, then x^2 < y^2. However, if x = -100 and y = 1, then x^2 > y^2. Not sufficient.
(2) x > 0
Combining the above with x < y, we get 0 < x < y. Now, since both sides of the inequality x < y are non-negative, then we can safely square and get x^2 < y^2. Sufficient.
Answer: B.
APPROACH 2:
If x < y, is x^2 < y^2 ?
Taking the square root of x^2 < y^2, we get |x| < |y|. Hence, the question essentially asks whether y is further from 0 than x on the number line.
(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.
If x is between -y and y on the number line, the answer will be YES:
--------(-y)--------0--------y--------
However, if x is to the left of -y (or is equal to it), on the number line, the answer will be NO:
--------(-y)--------0--------y--------
Not sufficient.
(2) x > 0
Combining the above with x < y, we get 0 < x < y. This implies that y is indeed further from 0 than x on the number line. Sufficient.
Sufficient.
Answer: B.
Hope it helps.
If x < y, is x^2 < y^2 ?
(1) y > 0
We are given that y is positive but we don't know the sign of x. If x = 0 and y = 1, then x^2 < y^2. However, if x = -100 and y = 1, then x^2 > y^2. Not sufficient.
(2) x > 0
Combining the above with x < y, we get 0 < x < y. Now, since both sides of the inequality x < y are non-negative, then we can safely square and get x^2 < y^2. Sufficient.
Answer: B.
APPROACH 2:
If x < y, is x^2 < y^2 ?
Taking the square root of x^2 < y^2, we get |x| < |y|. Hence, the question essentially asks whether y is further from 0 than x on the number line.
(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.
If x is between -y and y on the number line, the answer will be YES:
--------(-y)--------0--------y--------
However, if x is to the left of -y (or is equal to it), on the number line, the answer will be NO:
--------(-y)--------0--------y--------
Not sufficient.
(2) x > 0
Combining the above with x < y, we get 0 < x < y. This implies that y is indeed further from 0 than x on the number line. Sufficient.
Sufficient.
Answer: B.
Hope it helps.
General Discussion
gmatchile
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23 Jul 2015, 19:58
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, 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.
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.claudio hurtado
GMAT GRE SAT MATH Tutor in Chile
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