If m and n are prime numbers, what is |m-n|?

Question

If m and n are prime numbers, what is the value of |m-n|?

(1) m + n is a prime number.

(2) Both m and n are less than 5.

fauji · Answer

Approach

Given: m and n are prime numbers.

(S1):  m - n is a prime number:
- Multiple possibilities:
 if m = 5, n = 3 then |m-n| = |5-3| = 2
 if m = 5, n = 2 then |m-n| = |5-2| = 3 ..... Insufficient

(S2):  Both m and n are less than 5(2 and 3)
- Multiple possibilities:
 if m = 3, n = 2 then |m-n| = |3-2| = 1
 if m = 3, n = 3 then |m-n| = |3-3| = 0 ..... Insufficient

Combine S1 and S2: 
- E.g. Case: if m = 3, n = 2, |m-n| = |3-2| = 1, it is Non-Prime. ..... Insufficient 
No other possibility.

IMO  Option E

Raxit85 · Answer

If m and n are prime numbers, what is |m-n|?
(1) m - n is a prime number.
(2) Both m and n are less than 5.

Values of m and n = 2/3/5/7/11/13/17/19....... as they are prime numbers.
(1) m - n is a prime number.
If, m = 5 and n=2, then m-n=3, which is prime. So, |m-n| = |5-2| = 3
m = 5 and n=3, then m-n=2, which is prime. So, |m-n| = |5-3| = 2.
No unique answer. Insufficient.

(2) Both m and n are less than 5.
m = 2/3 and n = 2/3,
If, m = 2 and n = 3, |m-n| = |2-3| = 1.
m = 3 and n = 3, |m-n| = |3-3| = 0.
No unique answer. Insufficient.

1) + 2), both m and n are prime and less than 5. Additionally, m-n should be prime number.
If, m = 3 and n = 2, then m-n is not prime.
m= 2 and n = 2, then m-n is not prime. So, there is no such numbers which can satisfy the given conditions. Hence, combining two statements does not give answer.

Hence, E.

lacktutor · Answer

If m and n are prime numbers, what is the value of |m-n|?

( Statement1 ): m - n is a prime number.
--> m-n = 7-2 =5 (prime) --> |m-n|= |7-2|= 5
--> m-n= 5-3=2 (prime) --> |m-n|= |5-3|= 2
Insufficient

( Statement2 ): Both m and n are less than 5. (5 is not inclusive)
|m-n|= |3-2|= 1

--> but what if both m and n are the same prime numbers
|m-n|= |3-3|= 0 
|m-n|= |2-2|= 0
Insufficient

Taken together 1&2, 
 both m and n are less than 5--> m and n could be either 3 or 2-- but m-n≠ cannot be prime number. 
--> I would say that it is Insufficient

The answer is E.

hiranmay · Answer

If m and n are prime numbers, what is the value of |m-n|?

(1) m - n is a prime number. -->  insufficient: if m = 5 & n=3, m-n = 2, but if m = 5 & n=2, m-n = 3

(2) Both m and n are less than 5. -->  insufficient: if m = 3 & n=3, m-n = 0, but if m = 3 & n=2, m-n = 1

combining (1) & (2), we can't find any combination of m & n that satisfies both (1) & (2), so insufficient
 Answer: E

AndreV · Answer

1) Insufficient
Since all the prime numbers greater than 2 are odd, their summation would yield an even number, ruling out the possibility of obtaining a prime number. In order for the summation to be a prime number, one of the numbers needs to be even and the other hast to be odd. For instance,
if m=2 and n=5, then m+n=7 (prime). Therefore, |m-n|=3
if m=2 and n=3, then m+n=5 (prime). Therefore, |m-n|=1
2) Insufficient
if m=2 and n=2, then m-n=0. Therefore, |m-n|=0 {no specification as to whether m and n are different number)
if m=2 and n=3, then m-n=-1.Therefore, |m-n|=1
1)+2) Sufficient
the only set of prime number less than 5 are 2 and 3. Since both m and n cannot be equal as their summation would be an even number (therefore not prime), the only possible combinations are m=2 and n=3 or m=3 and n=2. Either way, |m-n|=1.
Answer: C

GMATBusters · Answer

Official Solution: 
St1: m+n = prime
Now if m =2, n = 3: 2+3 = 5 = prime 
|m-n|= |2-3|= 1
if m= 11, n =2: 11+2= 13 = prime
|m-n|= |11-2|= 9 
Two different answers, hence insufficient.

St1: Both m and n are less than 5.
hence m and n are from the set {2,3}
 but there can be case when both are equal 
m=n=2 or m=n=3: |m-n|= |2-2|= 0
or m =3,n= 2 ,|m-n|= |3-2|= 1
Two different answers, hence insufficient.

Combining both statement, we get 
 m cannot be equal to n , because otherwise m+n = 2m which is not prime 
hence, or m =3,n= 2 or m =2, n = 3 ,|m-n|= |3-2|= 1
Unique answer, Hence Sufficient.

Answer = C

OJA · Answer

Please share the official explanation for C ? I think the answer should be "B".

Bunuel · Answer

Valid solutions are already provided earlier in the thread. The answer is  not B  because if  m  and  n  are  different  primes, then |m - n| = 1, but if  m  and  n  are the  same  prime (which is allowed unless stated otherwise), then |m - n| = 0.

Remember: unless explicitly restricted, different variables can represent the same value.

Also note that pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

AVMachine · Answer

1. Observe, we only have one even prime no. i.e. 2, all the other primes are odd, so even + odd = odd and odd + odd = even (Can't be prime for value > 2)

So, we have only two combinations: 2 + 3 = 5 and 2 + 5 = 7; due to the two combinations, its not sufficient.

2. both prime less than 5; 2 - 2; 2 - 3; 3 - 3; again three combination; not sufficient;

Together: 2 - 3 = 1; Sufficinet.

If m and n are prime numbers, what is |m-n|?

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