Remainder problems are a unique type of question that pops up on the ACT® Math section. While they don't appear on every test, you'll likely encounter them on most ACTs®.
These questions might seem tricky at first, but they're actually pretty simple to solve when you know how they work.
"Remainder" questions are interesting because they're not typically taught in school. They're the kind of questions that feel like they were designed specifically for standardized tests.
These questions usually only require 2-3 steps of basic division, even though they often show up after question 30, where you'd expect more challenging concepts.
If it helps, you can think of remainder problems as cousins to LCM (Least Common Multiple) and GCF (Greatest Common Factor) questions. They're all about division and what's left over.
Let's look at some examples to see how these questions work in practice.
Consider this example:
Example 1:
can be written as . What is the 333rd digit?
To solve this, we need to look at the repeating sequence "142857". It has a length of 6 digits.
- Determine the position within the repeating sequence:
- Calculate the remainder when 333 is divided by 6.
- remainder .
- Identify the digit at the position given by the remainder:
- The remainder is 3, so the 333rd digit corresponds to the 3rd digit in the repeating sequence "142857".
Therefore, the 333rd digit is 2.
Example 2:
Today is Tuesday. What day is it 359 days from now?
- Determine the number of days in a week:
- There are 7 days in a week.
- Calculate the remainder when 359 is divided by 7:
- remainder .
- Add the remainder to the current day:
- Starting from Tuesday, add 2 days.
- Tuesday + 2 days = Thursday.
Therefore, 359 days from today will be Thursday.
How this is going to show up on the test?
These questions typically appear in one of two ways – either dealing with repeating decimals (like in Example 1) or with days of the week (like in Example 2). The key is to use division and find the remainder.