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

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Source: — Data Sufficiency |
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Re: If \(m\) and \(n\) are positive integers and \(mn = k,\) is \(m + n = k + 1?\)

by deloitte247 » Sat Jul 11, 2020 9:06 am

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B

C

D

E

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Target question => is m + n = k + 1 ?


Given that mn = k
m + n = k + 1
m + n = mn + 1
m + n = mn - 1 = 0
m - 1 = mn + n = 0
(m-1) - (mn-n) = 0
(m-1) -n (m-1) = 0
(m-1) - (1-n) = 0
m - 1 = 0 or 1 - n = 0
m = 1 or - n = -1
m = 1 or n = 1
For m + n = k + 1; n = 1


Statement 1 => m = 1
This information satisfies what we deduced from the target question so m + n = k + 1
Statement 1 is SUFFICIENT


Statement 2 => k is a prime number
Since mn = k, mn is also a prime number
k as a prime number is only divisible by 1 and itself. Definitely, k is a product of 1 and any other number
Given that k is a product of mn, either m or n equals to 1; this information satisfies what we deduced from the question stem. So, m + n = k + 1
Statement 2 is SUFFICIENT


Since each statement alone ARE SUFFICIENT
Answer = D
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