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

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EMBA Programs Moderator
Joined: 03 Apr 2019
Posts: 34
Location: United States (CA)
GPA: 3.75
If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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07 Aug 2019, 14:34
2
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Difficulty:

45% (medium)

Question Stats:

62% (01:32) correct 38% (01:36) wrong based on 422 sessions

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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.
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1888
Location: India
Re: If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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07 Aug 2019, 15:18
2
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.
Intern
Joined: 30 Aug 2019
Posts: 9
Re: If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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10 Sep 2019, 20:28
nick1816 wrote:
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.

Can you please elaborate on the second statement? I'm not able to understand the reasoning behind it.
Intern
Joined: 07 Nov 2018
Posts: 1
Location: Russian Federation
Re: If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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07 Oct 2019, 10:47
Quote:
Can you please elaborate on the second statement? I'm not able to understand the reasoning behind it.

GurkiD,

If k is a prime number, then it is a product of 1 and some other number, so either m or n equals to 1.
Manager
Joined: 23 Jul 2019
Posts: 173
Location: Austria
GPA: 3.9
Re: If m and n are positive integers and mn = k, is m + n = k + 1?  [#permalink]

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04 Feb 2020, 00:38
nick1816 wrote:
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.

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.

How do you derive from the upper line to the one below (marked in red)
Thanks
_________________
Let's get some
Re: If m and n are positive integers and mn = k, is m + n = k + 1?   [#permalink] 04 Feb 2020, 00:38