Reading Time: < 1 minute
Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We start by prime factoring 7,150.
7,150 = 715 x 10 = 143 x 5 x 10
At this point we must be careful. They WANT you to think that 143 is prime. Using our divisibility rules, however, we can determine that 143 is divisible by 11. A number is divisible by 11 if the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11. We can test 143 to prove this:
1 + 3 – 4 = 4 – 4 = 0
Since zero is divisible by 11, we know that 143 is divisible by 11. We can now finish the prime factorization.
143 x 5 x 10 = 11 x 13 x 5 x 5 x 2
11 x 13 x 5^2 x 2
Thus we can see that there are 4 different prime factors in 7,150.
Answer: D
