Data Sufficiency

If each of the two digits \(X\) and \(Y\) is distinct, is the two-digit integer \(XY\) prime?

(1) Each of the digits \(X\) and \(Y\) is the sum of \(2\) distinct single digit prime numbers.

(2) The sum of digits \(X\) and \(Y\) is \(16.\)

Answer: B

Source: Princeton Review

Target question => Is the two-digit integer XY prime?


Statement 1 => Each of the digits X and Y is the sum of 2 distinct single digit prime numbers
This means digits X and Y can be either 5, 7, 8, or 9. So if XY = 57 then the two-digit is not a prime but if XY = 59, then the two-digit is a prime number
Since the answer is not definite, statement 1 is NOT SUFFICIENT


Statement 2=> The sum of digits X and Y is 16
Two numbers between 0 and 9 in which their sum equals 16 are 7 and 9 or 9 and 7, or 8 and 8. So possible two-digit integer are 7,9 and 9,7
Both 7,9 and 9,7 are prime numbers so the two-digits XY are prime.
Statement 2 is SUFFICIENT


Answer = B