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If m and n are positive integers and mn = k, is m + n = k + 1?

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Intern
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Joined: 03 Apr 2019
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Location: United States (AZ)
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If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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New post 07 Aug 2019, 15:34
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If m and n are positive integers and mn = k, is m + n = k + 1?

(1) m = 1

(2) k is a prime number.
Director
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Joined: 19 Oct 2018
Posts: 791
Location: India
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Re: If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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New post 07 Aug 2019, 16:18
1
If m+n=mn+1
m+n-mn-1=0
(m-1)-(mn-n)=0
(m-1)-n(m-1)=0
(m-1)(n-1)=0
Either m or n is equal to 1, or both are equal to 1.

Statement 1-
m=1
Hence (m-1)(n-1)=0
Sufficient.

Statement 2-
k=mn=prime number
Hence either m or n must be equal to 1, as both are positive integers.
Again we get, (m-1)(n-1)=0
Sufficient

D

carbazzy wrote:
If m and n are positive integers and mn = k, is m + n = k + 1?

(1) m = 1

(2) k is a prime number.
GMAT Club Bot
Re: If m and n are positive integers and mn = k, is m + n = k + 1?   [#permalink] 07 Aug 2019, 16:18
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If m and n are positive integers and mn = k, is m + n = k + 1?

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