GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 10:41

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58395
If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

Show Tags

24 Jun 2017, 08:04
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:16) correct 33% (02:12) wrong based on 94 sessions

HideShow timer Statistics

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

_________________
Intern
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]

Show Tags

24 Jun 2017, 08:15
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.

Sent from my SM-N900 using GMAT Club Forum mobile app
Intern
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]

Show Tags

08 Jul 2017, 01:13
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.

_________________
Regards,
Sarugiri
Senior Manager
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]

Show Tags

08 Jul 2017, 04:40
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.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager
Joined: 03 Sep 2018
Posts: 179
Re: If r > t and r < 1 and rt = 1, then which one of the following must be  [#permalink]

Show Tags

18 Jan 2019, 09:06
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 $$t<-1$$

Re: If r > t and r < 1 and rt = 1, then which one of the following must be   [#permalink] 18 Jan 2019, 09:06
Display posts from previous: Sort by