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

Question

(1) m = 1

(2) k is a prime number.

nick1816 · Answer

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

GurkiD · Answer

Can you please elaborate on the second statement? I'm not able to understand the reasoning behind it.

Nelli · Answer

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.

chrtpmdr · Answer

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

acespedes94 · Answer

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

acespedes94 · Answer

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

deepakbarchha1 · Answer

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.  . 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

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=g7GCbrKbwfY Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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

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