If r t and r

Question

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

sejalvarshney · Answer

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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sarugiri · Answer

Given that t

TimeTraveller · Answer

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.

SchruteDwight · Answer

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

TestPrepUnlimited · Answer

Chain the two inequalities to find t < r < 1 , thus we have t < 1 . From rt = 1 , we can also infer r and t must be both positive or both negative. If r is positive, multiply both sides of t < 1 by r to get rt < r and r > 1 , which contradicts the earlier information. Then we can conclude r (and t consequently) must be negative. Multiply both sides of r > t by t to get rt < t^2 and 1 < t^2 . We can only take the negative solution of this, t < -1 . Since r has to be negative, among the answers we can only pick B. Ans: B

findingmyself · Answer

Take R=-3/4 and T=-4/3

Satisfied all condition, Check on answer choices, Only B fits the condition

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

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