Bunuel wrote:

If x and z are positive integers, is at least one of them a prime number?

(1) x^2 = 15 + z^2

(2) (x − z) is a prime number

Lets deal with Statement 1 first using plugin approach:

1 x^2 = 15 +z^2

2 we can write above statement as

x^2-Z^2=15 or (x+z)(x-z)=15

3. x+z= 3 means- 1 + 2=3 and x-z means- 4-1

4. so (1,2) and (4,1) -leads to insufficent we have 2 answers

A insufficient

II. Lets move on to 2nd statement

1. x-z is prime number

2. put x=4 , z=1 , none are prime , 4-1=3 , which is prime, so we got 1 no answer

3. put x=5 , y=2, both are prime, 5-2=3, which is prime, so we got 1 yes answer

So clearly B is insufficent

III. combining Statement 1 and statement 2

a)x^2-z^2=15

b) x-z =prime

if you plug values (4,1), both satisfies statement a and b,

if you try value like(5,2) , or any other combination, it wont satisfy both

hence A and B combined are sufficnet

Correct answer: C

Bunuel, please correct my approach if i m wrong

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