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If 1 < mn < 0, then which of the following can be true? m < 0 and n

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Carcass
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If 1 < mn < 0, then which of the following can be true? m < 0 and n [#permalink] New post   23 Mar 2022, 02:00
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If –1 < mn < 0, then which of the following can be true?

Indicate all that apply

m < 0 and n < 0
m < 1 and n < 1
m > 1 and n < –1
m > 1 and n > 1
–1 < m < 0 and n < 0

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B
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If 1 < mn < 0, then which of the following can be true? m < 0 and n [#permalink] New post   28 Mar 2022, 01:19
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Carcass wrote:
If –1 < mn < 0, then which of the following can be true?

Indicate all that apply

m < 0 and n < 0
m < 1 and n < 1
m > 1 and n < –1
m > 1 and n > 1
–1 < m < 0 and n < 0



\(–1 < mn < 0\)

i.e. \(mn\) is a -ve number
So \(m\) and \(n\) must have opposite signs
Eliminate option A, D, and E

Now between B and C

B. m < 1 and n < 1
Let \(m =\frac{1}{2}\) and \(n =\frac{-1}{2}\)
\(mn =\frac{-1}{4}\)

C. m > 1 and n < –1
Let us take the smallest values for \(m\) and \(n\)
Let \(m =1.001\) and \(n =-1.001\)
\(mn = -1.002\)

Hence, option B
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Re: If 1 < mn < 0, then which of the following can be true? m < 0 and n [#permalink] New post   24 Jul 2022, 23:17
KarunMendiratta wrote:
Carcass wrote:
If –1 < mn < 0, then which of the following can be true?

Indicate all that apply

m < 0 and n < 0
m < 1 and n < 1
m > 1 and n < –1
m > 1 and n > 1
–1 < m < 0 and n < 0



\(–1 < mn < 0\)

i.e. \(mn\) is a -ve number
So \(m\) and \(n\) must have opposite signs
Eliminate option A, D, and E

Now between B and C

B. m < 1 and n < 1
Let \(m =\frac{1}{2}\) and \(n =\frac{-1}{2}\)
\(mn =\frac{-1}{4}\)

C. m > 1 and n < –1
Let us take the smallest values for \(m\) and \(n\)
Let \(m =1.001\) and \(n =-1.001\)
\(mn = -1.002\)

Hence, option B


Sir, could you state your reasons for eliminating A, D, E
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Re: If 1 < mn < 0, then which of the following can be true? m < 0 and n [#permalink] New post   24 Jul 2022, 23:25
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It is not possible for m and n to be both negative or both positive, because this would make mn > 0, which is not the case. This rules out m < 0 and n < 0, m > 1 and n > 1, and –1 < m < 0 and n < 0. Furthermore, m > 1 and n < –1 is not possible because then the product mn would be less than –1, which is also not the case. Thus m < 1 and n < 1 is the only possibility which could be true.
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