DS w/ variable and prime #

[mwilliams82]

If M and N are positive integers and mn=k, M+N=K+1?

1. m=1

2. k is a prime number

The OA for this problem is D but statement two eludes me. Can anyone explain how 2 is sufficient?

Thanks

[itheenigma]

If M and N are positive integers and mn=k, M+N=K+1?

1. m=1

2. k is a prime number

The OA for this problem is D but statement two eludes me. Can anyone explain how 2 is sufficient?

Thanks

The answer seems right.
The problem states that k has 2 factors in 'm' and 'n'.
Now, according to statement 2, if k is a prime number, then either 'm' or 'n' has to be equal to 'k' and consequently, the other must be equal to 1 (prime number property).

In either case, M+N will be equal to K+1

[mwilliams82]

Yep. Thought it was something obvious that I was overlooking.

Thanks.

[RonPurewal]

If M and N are positive integers and mn=k, M+N=K+1?

1. m=1

2. k is a prime number

The OA for this problem is D but statement two eludes me. Can anyone explain how 2 is sufficient?

Thanks

The answer seems right.
The problem states that k has 2 factors in 'm' and 'n'.
Now, according to statement 2, if k is a prime number, then either 'm' or 'n' has to be equal to 'k' and consequently, the other must be equal to 1 (prime number property).

In either case, M+N will be equal to K+1

nicely done.

[jp.jprasanna]

HI I just have 1 question. What is the significance of "If M and N are positive integers" this constrain doesn't seem to have any effect on the answer?

Cheers

[RonPurewal]

HI I just have 1 question. What is the significance of "If M and N are positive integers" this constrain doesn't seem to have any effect on the answer?

Cheers

the effect is huge. if you take that statement away, you've got a completely different problem on your hands.

without that constraint, the answer to the question becomes (a). the effect of statement 1 is unchanged, but statement 2 doesn't work anymore.
for instance, if you have k = 5 in statement (2) without the "positive integers" restriction, then you can let m = 1 and n = 5 (a "yes" answer to the question), or you can let m = n = √5 (a "no" answer to the question).

in fact, the answer changes to (a) even if you just take away the word "positive" -- that is, even if you have the restriction "m and n are integers" rather than positive integers.
in that case, still with k = 5, you can let m = 1 and n = 5 (a "yes" answer to the question), or you can let m = -1 and n = -5 (a "no" answer).