GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 May 2020, 15:42 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is m+n prime?

Author Message
TAGS:

### Hide Tags

Retired Moderator V
Joined: 27 Oct 2017
Posts: 1780
WE: General Management (Education)

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 60% (01:42) correct 40% (01:41) wrong based on 31 sessions

### HideShow timer Statistics

Is m+n prime?
1) The difference between any two distinct positive factors of m is odd.
2) The difference between any two distinct positive factors of n is even.

_________________
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1780
WE: General Management (Education)

### Show Tags

Official Solution

St1) If the difference between any two positive factors is odd means one of the factors is Even and other is Odd.

We know, that 1 is a factor at all the integers. thus, to get the difference between any two positive factors is odd, we need another factor which is even

Only for 2, the factors would be 2 and 1 => difference as 1 = odd
hence, m = 2

NOT Sufficient

St 2) As per statement 2, n can be any odd integer.
NOT Sufficient

Even after combing
m=2, n = 5: m+n = 7 Prime
m=2, n = 7: m+n = 9 Not Prime
NOT Sufficient

_________________
Director  P
Joined: 14 Dec 2019
Posts: 657
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)

### Show Tags

Is m+n prime?
1) The difference between any two distinct positive factors of m is odd.
2) The difference between any two distinct positive factors of n is even.

i) If the difference between any two positive factors is odd means one of the factors is Even and other is Odd.

Thus m has to be even, though m can be only 2 since for any other even number than 2 will have some factors which will both be even and thus the difference would be even in such cases.

Only for 2 the factors would be 2 and 1 => difference as 1 = odd

Insufficent as we don't know about n

ii) n can be any odd or even number For eg. 21 => 3 and 7 factors => difference = 4
m+n = 21+2 = 23 = prime
n can be 4 => Factors 2 and 4 => difference = 2
m+n = 4+2 = 6 = non prime

CEO  V
Joined: 03 Jun 2019
Posts: 2887
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)

### Show Tags

1) The difference between any two distinct positive factors of m is odd.
m = 2; Since difference between 2-1= 1 = odd
If m = odd ; m-1 = even
And if m=even; m-1 = odd but m-2=even
m = 2 is the only possibility
Since n is unknown
NOT SUFFICIENT

2) The difference between any two distinct positive factors of n is even.
If n = even ; n-1 = odd; NOT FEASIBLE
But if n =odd; n-1=even; odd number has odd factors; odd-odd =even
n may be any odd number
but m is unknown
NOT SUFFICIENT

(1) + (2)
1) The difference between any two distinct positive factors of m is odd.
m = 2; Since difference between 2-1= 1 = odd
If m = odd ; m-1 = even
And if m=even; m-1 = odd but m-2=even
m = 2 is the only possibility
2) The difference between any two distinct positive factors of n is even.
If n = even ; n-1 = odd; NOT FEASIBLE
But if n =odd; n-1=even; odd number has odd factors; odd-odd =even
n may be any odd number
m + n = 2 + odd = odd
If m=2 & n = 3 ; m+n=5 ; prime number
But if m=2 & n=7; m+n = 9; Not a prime number
NOT SUFFICIENT

IMO E
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern  B
Joined: 02 Dec 2019
Posts: 10

### Show Tags

1
Is m+n prime?
1) The difference between any two distinct positive factors of m is odd.
2) The difference between any two distinct positive factors of n is even.

Lets test some numbers -

2 --> factors are 1,2 --> differences between those factors is 1, odd
3 --> ... 1,3 --> ... even
4 --> ... 1,2,4 --> ... both even/odd
5 --> ... 1, 5 --> ... even
8 --> ... 1,2,4,8 --> ... both even/odd
9 --> ... 1, 3, 9 --> ... even
10 --> ... 1,2,5,10 --> even/odd
27 --> ... 1,3,9,27--> ... even

The ONLY number that meets statement (1) is 2. every other even number that could meet this requirement also has two as a factor, which doesn't meet the statement requirements. m = 2.

Statement (2) tells us that n could be any odd number, since it's factors will all be odd and the differences between those factors is even. n = odd.

So to rephrase the question with our known information... "is an odd number, plus two, prime?" 3+2=5= prime, but 13+2=5=not prime. Insufficient with both statements together --> answer is (e).
Director  V
Joined: 22 Feb 2018
Posts: 736

### Show Tags

Is m+n prime?

1) The difference between any two distinct positive factors of m is odd.
If, m = 2 (2.1) , 2-1 =1,
m= 6 (1,2,3,6), 6-1 = 5/ 3-1 = 2, not possible.
Means only 2 satisfies the condition of m. But we don't know n.
If, n= 1 , then m+n = prime and if n=2, then m+n = not prime. So insufficient.

2) The difference between any two distinct positive factors of n is even.
If, n = 3 (3,1) , 3-1=2
n = 5 (5,1), 5-1=4
n = 9 (1,3,9), 9-1=8/9-3=6/3-1=2
n= 11 (1,11), 11-1 = 10
n = 15 (1,3,5,15)
If, m= 0, and n=3, then m+n = prime and if m=1 and n=3 then m+n = not prime. So insufficient.

1) + 2)
m= 2 and n = 3 , then m+n = 5 =prime
m=2, n=5, then m+n = 7 =prime
m=2, n=9, then m+n = 11 =prime
m =prime, n = 15, then m+n = 17 =prime.
Same pattern repeats. So sufficient.
Ans. C
Manager  S
Joined: 14 Aug 2017
Posts: 68
Location: India
Concentration: Other, General Management
GMAT 1: 640 Q48 V29

### Show Tags

we have 2 and any prime number from statemtnt 2 . so answer is E
Intern  B
Joined: 24 Mar 2019
Posts: 18

### Show Tags

(E) Cannot say
The difference between two distinct positive factors is a multiple of the number itself.
1 implies m is odd, since the difference is odd
2 implies n can be odd or even, since the difference is even then it can be that either n is even or the multiple part is even
Even/Odd+Odd can be anything and hence we cannot say

Posted from my mobile device
Senior Manager  P
Joined: 30 Oct 2019
Posts: 367
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4

### Show Tags

(1) Number is 2, Difference between positive factors 1 and 2 is odd. We do not know n. Insufficient

(2) Number can be any prime, 3, 5, 7, 11

(1) + (2)
2+3 = prime
2+7 = 9 = not a prime
Insufficient Re: Is m+n prime?   [#permalink] 29 Mar 2020, 06:37

# Is m+n prime?  