If x and y are prime numbers, what is the value of |x-y|?

Question

(1) x + y is a prime number
(2) Both x and y are less than 5

M10-29

Bunuel · Accepted Answer

This is GMAT Club question and the answer is C.

If x and y are prime numbers, what is the value of |x-y|?

(1) x + y is a prime number. Clearly insufficient, consider x=3, y=2 and x=5, y=2.

(2) Both x and y are less than 5. Also insufficient, consider x=3, y=2 and x=3, y=3.  Notice that on the GMAT, unless it is explicitly stated otherwise, different variables CAN represent the same number. So, x=y is a valid scenario.

(1)+(2) Either x=3 and y=2 or vise versa. In any case |x-y|=1. Sufficient.

Answer: C.

P.S. Unless it is explicitly stated otherwise, different variables CAN represent the same number. So, x=y is a valid scenario.

subhashghosh · Answer

From (1) we have, one of A or B is 2, and the other one can be 3, 5, 11 etc., so (1) is not enough.

From (2), the only 2 prime numbers less than 5 are 2 and 3, so (2) is sufficient.

Hence the answer is B.

fluke · Answer

Q: |A-B|?

1. A=2, B=5; A+B=7; |A-B|=3
 A=2, B=3; A+B=5; |A-B|=1
NS

2. A=2,B=2; |A-B|=0
 A=2,B=3; |A-B|=1
 A=3,B=2; |A-B|=1
 A=3,B=3; |A-B|=0
NS

Combining 1 and 2;
 A=2,B=3; A+B=5; |A-B|=1
 A=3,B=2; A+B=5; |A-B|=1

Sufficient.

Ans: "C"

vivesomnium · Answer

statement 1: A + B is a prime integer- if sum of two prime integers is prime, one of them has to be 2( Prime nos. are all odd, except 2, and odd +odd is even, so to make A + B, at least one has to be even. only even prime is 2) However, there is no way to find the value of other prime, it can be any prime upto infininty, so a single value of |A-B| cant be established. Hence, insufficient.
2. Only integers less than 5 which are prime are 2 and 3. Absolute value of difference therefore has only one possible value (i.e.1)
Hence sufficient.
Answer : B

Eden · Answer

1. (GC) A and B are prime integers. What is |A - B|?
(1) A + B is a prime integer
(2) Both A and B are less than 5

my solution:
(1) A+B is a prime integer
 One of the prime number is 2 and the other could be any prime number such that A+B is also a prime number (for ex: 3,5,7,11 etc). Therefore |A-B| could be any value => not sufficient
(2) Both A and B are less than 5
 A and B could be 2 or 3, and A and B could be the same prime number . Therefore |A+B| could be 0 or 1. => not sufficient
 (1 and 2)
A and B are 2 different prime numbers less that 5 (that means 2 and 3) => sufficient

Spidy001 · Answer

Answer should be C for this one.

Question doesnt say that A and B are different.

1. Not sufficient

2,5 diff 3
 2,11 diff 9

2. Not sufficient

2,2 diff 0
 3,3 difff 0
 2 3 diff 1

together we know that a and b has to different , because a+b is prime. so sufficient.

Answer C.

ygdrasil24 · Answer

If A=2, B=2 , |A-B| = 0 
If A=2/3 , B=2/3, |A-B|= 1

So how is answer is B ? Should be C ?

Chiranjeevee · Answer

From 1. The value of A,B can be anything 2,3 or 2,5 or 2,17 so on.... Adding A+B we get a prime number with different values of |A-B|. Not sufficient.
From 2. Value of A,B must be 2,3 or 3,2 mod of their difference will always be 1. sufficient

srinidhi mishra · Answer

If x and y are prime numbers, what is the value of |x-y|?

(1) x + y is a prime number
(2) Both x and y are less than 5

1-x+y =PN 2 & 3, 2& 5, 2& 11, 2&17 etc 
x,y<5 i.e. 2&3 
B alone answers the question 
How come OA is C ?

Shiwangvictory123 · Answer

if x and y are prime number than combinations can be 2 and 3, 3 and 5

1: x+y is a prime number 
 it is possible in many cases 
 a) x=2,y=3
 b) x=2,y=7
 Not sufficient
2: Not sufficient
Combining both we see only one case which is x=2 and y=3
So Answer is C

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If x and y are prime numbers, what is the value of |x-y|?

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