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If r > t and r < 1 and rt = 1, then which one of the following must be

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If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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New post 24 Jun 2017, 07:04
00:00
A
B
C
D
E

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Question Stats:

67% (02:18) correct 33% (02:22) wrong based on 108 sessions

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If \(r > t\) and \(r < 1\) and \(rt = 1\), then which one of the following must be true?


(A) \(r > 0\) and \(t < –1\)

(B) \(r > –1\) and \(t < –1\)

(C) \(r < –1\) and \(t > –1\)

(D) \(r < 1\) and \(t > 1\)

(E) \(r > 1\) and \(t < 0\)

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Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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New post 24 Jun 2017, 07:15
This question can easily be solved with the help of elimination technique.
From the question we have:
1. 1>r>t
2. rt=1 (From this we can also conclude that either both are positive or both are negative and none can be 0)

(A) INCORRECT as r is positive and t is negative whereas both need to be of the same sign.

(C) INCORRECT because r>t and not vice versa.

(D) INCORRECT because t<r and r <1 thus t <1.

(E) INCORRECT because r <1.

Hence (B) is the correct answer.


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Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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New post 08 Jul 2017, 00:13
Given that t<r, r<1 and rt = 1;
Same can be re-written as t<r<1 and rt=1
When multiplication of 2 numbers are eq to 1 it has to be reciprocal's which is r.(1/r) = 1
Also by looking at the choices, only choice B and C has the value for r and t in -ve.
From the stem, since t < r only choice B matches the above condition. So choice B it is. :)

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Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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New post 08 Jul 2017, 03:40
Given:
(i) \(r < 1\) - option E can be eliminated

(ii) \(t < r\), so \(t < 1\) - option C and D can be eliminated

(iii) \(rt = 1\), so \(r\) and \(t\) are inverse of each other with \(r > t\) - option A can be eliminated

Hence option B is correct.
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Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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New post 18 Jan 2019, 08:06
My reasoning is as follows:

\(t<r<1\) and \(rt=1\) \(\implies\) \(\frac{r}{1}*\frac{1}{r} =1\)

as \(t<r<1\) \(\implies\) \(-1<r<0\) and \(t<-1\)

Answer thus: b
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Re: If r > t and r < 1 and rt = 1, then which one of the following must be   [#permalink] 18 Jan 2019, 08:06
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If r > t and r < 1 and rt = 1, then which one of the following must be

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