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

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carbazzy
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If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] 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.
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D
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nick1816
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   07 Aug 2019, 16:18
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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.
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GurkiD
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   10 Sep 2019, 21:28
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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.
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Nelli
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   07 Oct 2019, 11:47
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.
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chrtpmdr
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   04 Feb 2020, 01:38
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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
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   27 Aug 2021, 10:53
Considering that m and n are positive integers:

1) If m=1
Then mn=k is (1)n=k, so n=k. As a result m+n=k+1 is 1+n=n+1 (Sufficient)

2) k is a prime number, so the factors of k are 1 and k.

Considering this: m or n has to be equal to 1. Again we come up with the same answer.
Assuming m=1, (1)n=k (n is a prime number), and 1+n = n+1 (Sufficient)

Answer: D
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acespedes94
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If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   27 Aug 2021, 10:54
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Considering that m and n are positive integers:

1) If m=1
Then mn=k is (1)n=k, so n=k. As a result m+n=k+1 is 1+n=n+1 (Sufficient)

2) k is a prime number, so the factors of k are 1 and k.

Considering this: m or n has to be equal to 1. So we get the same answer as in 1).
Assuming m=1, (1)n=k (n is a prime number), and 1+n = n+1 (Sufficient)

Answer: D
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deepakbarchha1
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   28 Aug 2021, 00:56
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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.


Ans:

1. [m*n = k (given)]. If m = 1 then n = k (because 1*n = n = k . So 1 + n = k + 1. Sufficient.

2. If k is a prime number than k has only two factor i.e. number 1 and k (itself). So m * n = k, it means that either m or n has value 1. Thus sufficient.

IMO : D
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Re: If m and n are positive integers and mn = k, is m + n = k + 1? [#permalink] New post   13 Jan 2024, 20:08
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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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