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If x2 = a2, what cannot be true about x and a?
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05 Jan 2022, 12:04
05 Jan 2022, 12:04
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If \(x^2 = a^2\), what cannot be true about x and a?
(A) xa < 0
(B) x = -a
(C) x = a
(D) x + a < 0
(E) All of the statements are true
(A) xa < 0
(B) x = -a
(C) x = a
(D) x + a < 0
(E) All of the statements are true
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Re: If x2 = a2, what cannot be true about x and a?
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06 Jan 2022, 04:41
06 Jan 2022, 04:41
1
In a case like this, first consider the wording of the question: "what CANNOT be true..."
This means that if we can find a situation where the statement IS true, then this answer choice will not be valid.
Let's look for those cases:
a) either x or a could be negative and still have x^2 = a^2 be true. This CAN be true.
b) in this case, the absolute value of the number doesn't matter because x and a would have the same absolute value in any case -- you can refer to a) because the reasoning is the same. This CAN be true.
c) again, the absolute value of the number doesn't matter. This CAN be true.
d) this can work out to x < -a; just consider the case where a is negative and x is negative, for example a = -2 and x = -2. In this case, x < -a would be -2 < -(-2) or -2 < 2, which works. This CAN be true.
e) since we have proven that each of these cases CAN be true, E is the answer.
This means that if we can find a situation where the statement IS true, then this answer choice will not be valid.
Let's look for those cases:
a) either x or a could be negative and still have x^2 = a^2 be true. This CAN be true.
b) in this case, the absolute value of the number doesn't matter because x and a would have the same absolute value in any case -- you can refer to a) because the reasoning is the same. This CAN be true.
c) again, the absolute value of the number doesn't matter. This CAN be true.
d) this can work out to x < -a; just consider the case where a is negative and x is negative, for example a = -2 and x = -2. In this case, x < -a would be -2 < -(-2) or -2 < 2, which works. This CAN be true.
e) since we have proven that each of these cases CAN be true, E is the answer.
gmatclubot
Re: If x2 = a2, what cannot be true about x and a? [#permalink]
06 Jan 2022, 04:41
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