If m and n are positive integers and m + n is prime, is m

Question

If m and n are positive integers and m + n is prime, is m odd?

(1) n is an odd number.
(2) n is greater than 2.

Bunuel · Answer

If m and n are positive integers and m + n is prime, is m odd?

(1) n is an odd number --> if  n=1  then  m  can still be even as well as odd:  m=1=odd  -->  m+n=2=prime  or  m=2=even  -->  m+n=3=prime . Not sufficient.

(2) n is greater than 2. Clearly insufficient.

(1)+(2) As  n=odd>2 , then  m+n=prime>2  so this prime is odd -->  m=even . Sufficient.

Answer: C.

loveparis · Answer

great) thanks a lot=)

ShalabhAr · Answer

Just came across this question.

In statement A, is it not incorrect to take n=1. 1 is not an odd number right?

Bunuel · Answer

An odd number is an integer which is not evenly divisible by 2 , so 1 is definitely an odd number. Check Number Theory chapter of Math Book for more: math-number-theory-88376.html Hope it helps.

ShalabhAr · Answer

My bad, if the OG calls it odd, it has to be odd. :-|

Although 1 is supposed to be a unique number.

Bunuel · Answer

OG has nothing to do with it. 1 is an odd number according to the definition of odd numbers in math.

ShalabhAr · Answer

In our side of the world, we were taught of it as a unique number that has hung on to me till now. Though i agree with the above definition. Thanks.

ratinarace · Answer

Hi Bunuel

Just a simple question? It could be dumb though..How can M and N both be 1? arent they both supposed to be two different numbers?

Bunuel · Answer

Unless otherwise specified , variables could represent the same number.

krrish · Answer

S1: n can take values from 1 can have 3, 5, 7, 11 if we take 1 then m can have 1 to make 2 or 2 to make 3 so : NS
s2: if n is > 2 so n can be 3, 4 and m can have 2 and 3 in for both so even/ odd : not sufficient.
 now combine both of them s1 and s2 = > n is odd and n>2 so it can have only add and m should be even to keep it prime so sufficent C

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If m and n are positive integers and m + n is prime, is m

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If m and n are positive integers and m + n is prime, is m

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