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sivaelectric
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Hi!sivaelectric wrote:If X^3 > Y^4, which of the following CANNOT be true?
- A. X<1
B.X+Y<0
C.0<XY<1
D.X(Y^2)<0
E.X=|X|
We know that y^4 must be non-negative. So, from the original inequality we know that x^3 must be positive. Accordingly, we can conclude that x is positive.
With that in mind, since we want an answer that CANNOT be true, let's look for a choice that requires x to be non-positive.
A) nope
B) nope
C) nope
D) ding ding ding! In order for x(y^2) to be negative, one of the two terms would have be negative. Since y^2 is definitely non-negative, in order for (D) to be true x must be negative.
However, we've already shown that x must be positive, so (D) CANNOT be true... choose (D)!
* * *
Note that we also could have attacked this question by picking numbers. When a question asks which of the following CANNOT be true, we want to pick numbers to show that an answer COULD be true; as soon as we do so, we can eliminate that choice.
Statistically, (D) and (E) show up more often than they should on problem solving questions with "which of the following" in the stem. So, when we work with the choices we should go bottom up.
E) x=|x|
If x=10 and y=1, then 10^3>1^4 and 10=|10|. (E) could be true: eliminate it.
D) x(y^2)<0
we know that y^2 can't be negative, so x must be negative to make this statement true.
if x = -1 and y = 1, then x^3 = -1 and y^4 = 1. However, -1 is NOT > 1, so we can't pick these numbers.
We should pretty quickly see that there are no numbers which satisfy both (D) and the original inequality, making (D) our CANNOT be true... choose (D)!
