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Inclusive Counting

Mike McGarry
Lesson by Mike McGarry
Magoosh Expert
Summary
The essence of the content revolves around the concept of inclusive counting, a crucial mathematical technique especially pertinent for GRE exam preparation. It elucidates how to accurately count the number of items or days between two points when both endpoints are included.
  • Inclusive counting is used when both the starting and ending values in a range are to be included in the count.
  • The process involves performing ordinary subtraction of the two values and then adding one to include the starting value.
  • This technique is contrasted with ordinary subtraction, which automatically excludes the lower endpoint.
  • Examples provided include calculating the number of days in a workshop, the duration of contract negotiations, and counting multiples of a number within a specified range.
  • Understanding and applying inclusive counting correctly is essential for solving certain types of quantitative problems on the GRE.
Chapters
00:00
Introduction to Inclusive Counting
00:31
Contrasting Inclusive Counting with Ordinary Subtraction
03:41
Inclusive Counting with Multiples

FAQ: I can’t remember how many days are in each month of the year. Will I need to know this for the test?

A: It’s highly unlikely that you’d have to know this. If there’s a question on the test where you need to know how many days are in a certain month, the information would probably be given as part of the problem.

However, if you want to be hyper-prepared for the test, and you want to be ready for any situation that might come up on the test (however unlikely), then you could learn how many days are in each month (here’s a poem that will help). Otherwise, don’t worry about this – it’s VERY unlikely that you’ll need to know it!

FAQ: For the last example (multiples of 8 between 200 - 640 inclusive), I subtracted 200 from 640, divided by 8 and then added one. Is this a valid strategy?

A: Yes, this method works!

You need to be careful, though: how did you know to add 1? That’s the correct thing to do here, but make sure you're not off by 1 in your final answer. One way to double check is to use small numbers/intervals that you can count directly as well to verify. For example:

How many multiples of 5 are there between 20 and 10 inclusive?

Just by counting, we know there are 3: 10, 15, 20

20 - 10 = 10

Divide by 5 = 2

2 + 1 = 3 

OK, so we confirmed that adding 1 should give us the correct result. So you add 1 to 55 in this case.

It’s always a good idea to check with smaller numbers if you're using a method like this!