2012-06-25 09:00:18

Keith's lottery number consists of three two-digit numbers. The number satisfies the following conditions:

- One number is even
- One number is a multiple of 7
- One number is prime

If each number satisfies exactly one of the conditions, which of the following could be Keith's lottery number?
A) 18 - 14 - 11
B) 44 - 21 - 31
C) 21 - 17 - 19
D) 28 - 21 - 13
E) 32 - 7 - 15

The correct choice is B

Explanation: The prompt states that each number (all of which must be two-digits) must satisfy only one condition. Check each answer choice, crossing off any that contain either a number that satisfies more than one condition or does not satisfy all three conditions:

(A) 18 - 14 - 11: This does not work because 14 is both a multiple of 7 and even.

(B) 44 - 21 - 31: 44 is even but not prime or a multiple of 7; 21 is a multiple of 7 but not even or a prime; and 31 is a prime but not even or a multiple of 7.

(C) 21 - 17 - 19: This does not work because it does not contain any even numbers.

(D) 28 - 21 - 13: This does not work because both 28 and 21 are multiples of 7, and 28 is both even and a multiple of 7.

(E) This does not work because 7 is not a two-digit number.

Choice (B) is correct, because it is the only answer that does not break a rule.