1. Time Yourself
2. Solve on a seperate sheet of paper
3. Write your solution here, and your time, please.
1/X+1/Y=36/323. Find X-Y.
(1) X and Y are primes
C is the correct answer.
Quoting Akamai here:
Restating the question stem, we get:
(X + Y)/(XY) = 36/323
(1) restricts X and Y to prime integers. With little experimentation, we can discover that 323 = 19 * 17, two prime numbers. Just by inspection, we can see that X and Y can be 19 and 17 or 17 and 19 respectively and satisfy the equation. Moreover, since X and Y are primes, they are the ONLY solutions to the equation. However, we don't know which one is which so we cannot ascertain what X-Y is. Hence (1) is NOT sufficient and we must eliminate A and D.
(2) tells us that X > Y and both are positive. However, it does not restrict the solution to prime number, or even integers. Hence, there are probably an infinite number of solutions to the equation and (2) is also not sufficient and we must eliminate B.
Using both, (1) tells us that X and Y must be 17 & 19 or 19 and 17, and (2) tells us that X is larger, so we now know which solution is the correct one and we can answer the question. Hence, the correct answer is C.