Hard GRE Math Comparison Problem with Solution Yesterday I posted a Level 4 GRE math comparison problem. Click the following link to see that post: Hard GRE Math Comparison Problem Some of you already figured out how to solve this one. Today I will provide a solution to the problem. Level 4 Arithmetic Comparison Problem p is a prime number greater than 2. Quantity A: The number of distinct prime factors of 27p Quantity B: The number of distinct prime factors of 49p A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. * Solution by picking numbers: If we let p = 3, then 27p = 27 ⋅ 3 = 34, and 49p = 49 ⋅ 3 = 3 ⋅ 72. So Quantity A is 1 and Quantity B is 2. Therefore, Quantity B is greater than Quantity A. Now, if we let p = 7, then 27p = 27 ⋅ 7 = 33 ⋅ 7, and 49p = 49 ⋅ 7 = 73. So Quantity A is 2 and Quantity B is 1. Therefore, Quantity A is greater than Quantity B. So the answer is D. Notes: (1) The only prime factor of 27 is 3 (27 = 33), and the only prime factor of 49 is 7 (49 = 72). So it seems natural to try 3 and 7 for p. (2) If we choose any number for p other than 3 or 7, then Quantities A and B will be the same (they will both be equal to 2). Try setting p = 5, for example. I leave the details to the reader. More GRE Math Problems If you are preparing for the GRE, you may want to check out 320 GRE Math Problems. Click on the image below to get to the book’s Amazon page: If you liked this article, please share it with your Facebook friends: And don’t forget to check out my social media pages: Comments comments