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Bunuel
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x, y, r, and t are integers such that x^y is negative and 09 Mar 2023, 11:45
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55% (hard)

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66% (01:49) correct 34% (01:57) wrong based on 306 sessions

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x, y, r, and t are integers such that \(x^y\) is negative and \(r^t\) is positive. If t is not a multiple of 2, then which of the following statements must be true?

(A) xr > 0
(B) x − r < 0
(C) y is a multiple of 2
(D) x^t > 0
(E) None of the above
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B
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stne
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x, y, r, and t are integers such that x^y is negative and 13 Mar 2023, 11:08
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Bunuel
x, y, r, and t are integers such that \(x^y\) is negative and \(r^t\) is positive. If t is not a multiple of 2, then which of the following statements must be true?

(A) xr > 0
(B) x − r < 0
(C) y is a multiple of 2
(D) x^t > 0
(E) None of the above
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if \(x^y\) is negative then \(x\) must be negative and \(y\) must be odd ( but \(y\) could be \(-ve\) odd or \(+ve \) odd, although it doesn't matter in this question)

If \(r^t\) is positive and \(t\) is not a multiple of \(2\) then \(t\) is odd. Which means \(r\) must be \(+ve.\)

So we have \(x = -ve \) and \(r = +ve \)

\(x< r \)

Ans B

Hope it helps.
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DonBosco7
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x, y, r, and t are integers such that x^y is negative and 28 Jul 2025, 10:50
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I think this is a poor question.
I get that x = -ve and r = +ve
and when we write it like this x<r, then option (B) x-r<0 makes sense.

But if you put values into the same, you will find that no option is a must be true.

take B for example
x-r<0
1] -2+3<0 No
2] -5+3<0 yes
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x, y, r, and t are integers such that x^y is negative and 28 Jul 2025, 13:50
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DonBosco7
I think this is a poor question.
I get that x = -ve and r = +ve
and when we write it like this x<r, then option (B) x-r<0 makes sense.

But if you put values into the same, you will find that no option is a must be true.

take B for example
x-r<0
1] -2+3<0 No
2] -5+3<0 yes
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Let's take values

\( x =-2 \) and \(r =3 \)

Then \(x-r\) becomes:

\(-2-3 < 0\) Always True

B is SUFF.

Hope it helped.
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eeaimirza
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x, y, r, and t are integers such that x^y is negative and 29 Jul 2025, 07:41
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DonBosco7
I think this is a poor question.
I get that x = -ve and r = +ve
and when we write it like this x<r, then option (B) x-r<0 makes sense.

But if you put values into the same, you will find that no option is a must be true.

take B for example
x-r<0
1] -2+3<0 No
2] -5+3<0 yes
Show more


"Regarding the example, as per the expression, which is, x-r, we must to take only negative values for x and positive values for r (as derived from the question). Hence, putting x=-2 and y=+3 will result as below,

-2-(+3)=-2-3=-5<0. So the condition holds and the correct answer is B."
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