Question 5 of PrepSwift: NON Factors of Factorials

GRE Quant Problem Solving
1

This question asks: “What is the sum of the two smallest integers that are NOT factors of 20! and are also NOT prime numbers?”. The answer to this question is 104 which is obtained by the sum 46+58.

I think there are two problems with this question:

  1. There is no requirement that the two integers have to be positive. Other GregMat questions on the topic of factoring specify this restriction. Without this restriction, you can have a sum of infinitely small terms that are not factors of 20!.
  2. The question does not specify that the two integers have to be different. Since this restriction is not made, the sum of 46 and 46 is smaller than 104.
2
  1. Fixed.
  2. I don’t think that is a reasonable assumption to make - “two smallest” imply distinct.