Sum of Multiples

GRE Quant Problem Solving
1

Hi Everyone, How do you solve the "Sum of all multiples of 2 and multiples of 3 from 1 to 50, inclusive”?

In my notes below, I did this but I am confused where I am getting 26 (re: when I times it my the number of multiples of 2, and similar with mult of 3). Like when you find the number of multiples, what is the next step?

Would appreciate any help as my test is tomorrow.

  • Add multiples of 2 and 3 minus multiple of 6
  • Multiples of 2: (50 - 2)/2 = 48 / 2 = 24 + 1 = 25
    • Sum of multiples of 2: 26 * 25
  • (48 - 3)/3 = 15 + 1 = 16
    • 51 * 8
  • (48-6)/6 = 42/6 = 12
    • 54 * 4
  • therefore , 842
2

26 comes because you are basically trying to find how many pairs of 52 would exist.
So, based on your formula-
Step 1: Gives you number of multiples of 2
Multiples of 2: (50 - 2)/2 = 48 / 2 = 24 + 1 = 25
Step 2: To find the sum, you add first and last number since the series start from 2--------50. Adding first and last would give you 52. In this step, we are interested in finding how many pairs of 52 exist, since number of multiples are 25.

The final step would be 52.25/2 (note that dividing by 2 here means given the total number of multiples how many pairs can we make)
simplification gives you = 26.25

That is how you reach there. Hope it is clear now

3

Yes a bit clearer, for the final step I’m confused still. I understand how you got 52. Do you multiply 52 and 25 and divide that by 2? Which that would be 650 :confused:

4

yes.
650 is correct if we just have to find the sum of multiples of 2 from 1 to 50. In our case series would start from 2 to 50. What is the issue in this? I am unable to understand where are you confused. can you specifically point out.

I would say instead of learning the steps. Try to understand why are we doing this.
We have to find sum of this series right and we know that there is a pattern that the series follows if we start adding first and last pairs to get the sum.

2, 3, 4, 5, …46, 47, 48, 49, 50

  1. Add 50 + 2 = 52
  2. Add 3 + 49 = 52
  3. Add 4 + 48 = 52
    and it follows…

So, we want to understand how many such pairs exist right. For that we find number of multiples.
But for pairs contain 2 numbers together. So,to find the number of pairs you divide 25 by 2 and then multiply that by 52. This will provide you how many pairs of 52 exist in the series.

Let me know if this makes sense

1 Like
5

Thank you helpful!

However, you said 650 is right if it’s from 1-50. Followed the approach to find the sum of 2-50 and got the same answer. I feel like they’re synonymous. Is there supposed to be another answer besides 650?

6

Sorry I made a typo

I was saying that 650 is correct if we find the sum from 2 to 50. Here, 1 doesn’t make sense because it is not a multiple of 2. 650 is the only answer.