What are scenario types of math problems? They occur when there are basically no number in the question; instead, there are variables. The variables can have:
1) ranges
2) one variable can be related to another variable
3) the variables can be only certain types of numbers
1) The variables have ranges
Here are some examples of the 3 problem types below.
= + = + In order for this to be a large number, the numerator must be big and the denominator must be small. Therefore, x = 8 and y = 18 + = + = + = Answer: H
2) One variable is related to another variable
2a = 3b => a = 3/2b (a is bigger than b) (1/4)b = (1/2)c => b = 2c (b is bigger than c) c < b < a Answer: A
Set A = a₁ a₂ a₃ a₄ a₅
Set B = b₁ b₂ b₃ b₄ b₅
a₂ = b₂ & a₃ = b₃ & a₄ = b₄ & a₅ = b₅
a₁ < b₁
The mean must be greater because b₁ is larger than a₁
The median is the same because that's the middle number and a₃ = b₃ (assuming the numbers are put in order)
The range is smaller for set B than set A (range = largest - smallest value)
Answer: A
3) Variables can only be certain types of numbers
Given 4 consecutive positive integers: 1, 2, 3, 4 I. Prime number: 2, 3, 5, 7, 11, 13… => Yes, this is true II. Common Prime factor: 4 = 2 * 2 and 2 = 2 * 1 (2 is the common prime factor) => Yes, this is true III. 1 of the 4 integers is a factor of 1 of the other 3: 4 = 2 * 2 => Yes, this is true ---------------- Try 4 more numbers: 24, 25, 26, 27 I. Prime number: 2, 3, 5, 7, 11, 13… => No, this is not true II. Common Prime factor: 24 = 12 * 2 and 26 = 13 * 2 (2 is the common prime factor) => Yes, this is true III. 1 of the 4 integers is a factor of 1 of the other => No, this is not true Tricks to solve these problems
There’s a way to solve these problems. And it’s not that hard. You just need to learn the tricks.
Before you can start the problem, you need to know examples of the following types of numbers:
Real numbers: 5, 5.2222222, 6.3, 0, -1, -1.999
Integers: 7, 8, 0, -1, -5
Rational Numbers: 1.2, 5.7, 0, -1.3
Irrational Numbers: π, √3, 1.22222222222
Prime Numbers: 2, 3, 5, 7, 11, 13, 17, etc
1) Start by writing down information and what’s given. They say that x can be any positive even integer. Then write down: x = 2, 4, 6, 8. That’s it. The key is to keep is simple! Start with easy small numbers.
2) Test out the limits or put in a value for each of the different variables, given the conditions.
Most of the time, it’s not immediately obvious what the solution is or how to solve it. It’s kind of like peeling an onion; you just need to start peeling it to see what’s inside.
3) Try out each of the answer choices based on what’s given in the problem.
Yes, these sometimes take 1-2 minutes to complete. It’s best to write down your work and let the math lead you to the answer.
How many problems are there like this?
There’s around 2-4 of these types of problems on every test. They typically fall around questions 40 and beyond. However, the ACT has been putting them earlier in the test recently.
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