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# rt < 0 < -r

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rt < 0 < -r [#permalink]  21 Nov 2017, 12:56
Expert's post
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Question Stats:

73% (00:17) correct 26% (00:38) wrong based on 56 sessions
$$rt < 0 < -r$$

 Quantity A Quantity B t 0

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: rt < 0 < -r [#permalink]  28 Jan 2018, 07:07
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Explanation

here, -r > 0 hence r must be a -ve number for -ve*-ve = +ve
r*t<0 for this r*t = -ve number. r is already -ve so t must be a +ve number as -ve*+ve = -ve
(A)
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: rt < 0 < -r [#permalink]  29 Jan 2018, 15:39
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Expert's post
Carcass wrote:
$$rt < 0 < -r$$

 Quantity A Quantity B t 0

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

GIVEN: 0 < -r
So, -r is POSITIVE, which means r is NEGATIVE

GIVEN: rt < 0
In other words, rt is NEGATIVE
Since we know r is NEGATIVE, we can write (NEGATIVE)(t) = NEGATIVE
So, we can conclude that t is POSITIVE

We get:
Quantity A: POSITIVE
Quantity B: 0

Answer: A

Cheers,
Brent
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Re: rt < 0 < -r [#permalink]  20 Oct 2018, 06:20
I thought the ques is wrong as how -r can be greater than 0? So as per the explanation we will consider such numbers as positive??
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Re: rt < 0 < -r [#permalink]  20 Oct 2018, 06:38
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Reetika1990 wrote:
I thought the ques is wrong as how -r can be greater than 0? So as per the explanation we will consider such numbers as positive??

as $$−r>0$$ so r must be a negative number so that $$−(−ve)$$ becomes a positive number.

$$r∗t<0$$ so t must be a positive number, if t is −$$ve$$ then the product will not be lesser than 0.

So the answer is A.
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Re: rt < 0 < -r [#permalink]  20 Oct 2018, 07:17
Expert's post
Reetika1990 wrote:
I thought the ques is wrong as how -r can be greater than 0? So as per the explanation we will consider such numbers as positive??

As -(-1)>0 , since it turns into 1>0
The value of r is -1, so -(-1)=-(r)>0
r is a variable which can take any value- positive, negative, 0, integer or fraction..
You have to consider for all values unless it is specified which group does it belong to..
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: rt < 0 < -r   [#permalink] 20 Oct 2018, 07:17
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# rt < 0 < -r

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