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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If r > t and r < 1 and rt = 1, then which one of the following must be

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Math Expert V
Joined: 02 Sep 2009
Posts: 59039
If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 67% (02:17) correct 33% (02:12) wrong based on 95 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 $$t < 0$$

Source: Nova GMAT
Difficulty Level: 650

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Senior Manager  B
Joined: 28 Jun 2015
Posts: 283
Concentration: Finance
GPA: 3.5
Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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1
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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I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Intern  B
Joined: 14 Jun 2017
Posts: 4
Location: India
Schools: Duke Fuqua
GMAT 1: 690 Q50 V32 GPA: 3.79
Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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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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Intern  B
Joined: 22 Oct 2016
Posts: 21
Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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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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Sarugiri
Manager  B
Joined: 03 Sep 2018
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GMAT 1: 710 Q48 V40 GPA: 4
Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

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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 $$t<-1$$

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Good luck to you. Re: If r > t and r < 1 and rt = 1, then which one of the following must be   [#permalink] 18 Jan 2019, 09:06
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# If r > t and r < 1 and rt = 1, then which one of the following must be  