Multiples and Factor Help

GRE Quant Problem Solving
1

Hey y’all, I am working through flashcards group 1 quiz and there are several Quant Comparison that I need help with:

  1. the first question is find the number of factors of 2n and 3n. How do you solve this? (see attached for the problem)

  2. the second question is how do you find the number of multiple of a a number within a range (i.e., all the multiples of 2 from 1 to 50)?

  3. the third question is comparing the “largest factor of 200” and “the smallest positive multiple of 200” how do you solve it?

Thanks,
Haley

Screen Shot 2024-09-03 at 9.36.04 PM
Screen Shot 2024-09-03 at 9.36.04 PM1148×442 21.6 KB

2
  1. For first question:-> first take n =11 both have equal number of factors = 2x2 = 4, then take n =12 for which A has 4x2 = 8 factors and B has 3x3 = 9 factors so option D is correct.
  2. for second there’s a simple formula you can get it on the internet i don’t remember it exactly right now.
  3. largest factor of 200 will be 200 and smallest positive multiple of 200 will be 200x1 =200 so the answer is going to be 200-200 = 0
3

These can be solved if you watch solution video for this quiz but as it refreshes my memory I will explain.

  1. This is a QC problem so check for multiple scenarios. The best would be to use equal not equal strategy and choosing number.
    First, chose n value as a prime number like 11 then when you use 11 on Quantity A you get 22 which have 4 factors(1,2,11,22) and when you put 11 in quantity B you get 33 which have 4 factors too (1,3,11,33). So we can say these QA =QB
    Second, chose n value as a number which has lots of factors like 12 then when you substitute the value you get 24 which have 8 factors (2^3,3^1) but quantity B which becomes 36 has 9 factors (2^2, 3^2). So, QA<QB. Therefore, answer is D

  2. you can use formula [(last multiple(50) - first multiple(2))/given multiple(2)] + 1 which gives number of multiples of 2. There is simple formula in quant mountain you can check it.

  3. Largest Factor of 200 will always be 200 itself as 200 x 1 is possible. Then, smallest multiple is always Zero but as positive is said it will be again 200 x 1 = 200 itself.

1 Like