# Practice GMAT Problem Solving Question

The product of the prime integers between 43 and 50, inclusive, is:
 A) 50! – 40! B) 99,029 C) 2,303 D) 2,021 E) 2,000
1. To find the prime numbers between 40 and 50, inclusive, begin by eliminating all even numbers and multiples of 5.
Original List: 43, 44, 45, 46, 47, 48, 49, 50
Possible Primes Remaining: 43, 47, 49
2. Since 7*7 = 49, 49 cannot be a prime number since 7 is a factor.
Possible Primes Remaining: 43, 47
3. Apply the relevant divisibility rules to each number remaining.
43 will not be divisible by 3 since the sum of its digits is 7, which is not divisible by 3
43 will not be divisible by 6 since it is not divisible by 3
43 will not be divisible by 8 since it is not even
43 will not be divisible by 9 since the sum of its digits is 7, which is not divisible by 9

Since 7*6 = 42, you know 43 is not divisible by 7

43 is prime.

47 will not be divisible by 3 since the sum of its digits is 11, which is not divisible by 3
47 will not be divisible by 6 since it is not divisible by 3
47 will not be divisible by 8 since it is not even
47 will not be divisible by 9 since the sum of its digits is 7, which is not divisible by 9

Since 7*7 = 49, you know 47 is not divisible by 7

The only number remaining is 49, which is not prime since 7*7 = 49
4. Having determined the prime numbers, you can multiply them together:
43*47 = 2,021