# Practice GMAT Problem Solving Question

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The product of the prime integers between 43 and 50, inclusive, is:

Correct Answer:

**D**- 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 - Since 7*7 = 49, 49 cannot be a prime number since 7 is a factor.

Possible Primes Remaining: 43, 47 - 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 - Having determined the prime numbers, you can multiply them together:

43*47 = 2,021

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