When you encounter a question on the ACT Math Test that you don’t know how to solve, what do you do? Even if your Math skills are strong, you’re likely to see at least a couple of challenging questions on the ACT Math Test. Sometimes doing the Math is not always the best way to get to the correct answer – a strategy like Picking Numbers or Backsolving can be preferable. You can also use Approximation & Estimation on difficult test questions; this is especially helpful when you’re running out of time, or for questions where there is no applicable formula. Let’s look at how we can use this in our Test Prep to get better ACT scores on Test Day.
Figure ABCDE was drawn on a grid of unit squares, with each vertex at the intersection of two grid lines. What is the area of the figure in square units?
A 19
B 23
C 25
D 27
E 33
Since there is no formula to solve for the area of this 5-sides figure, we know that Approximation will be our best strategy here. The way to find the area of this figure is to divide it into sections, first counting the full squares, then the half squares, then the pieces of square.
Whole squares (blue) = 19 full squares
Half squares (green) 2 = 1 full square
Grey pieces = 1 full square
Pink pieces = 1 full square
Purple pieces = 1 full square
Adding together all the areas gives a total of 23 square units. The answer is (B).
When you approximate, let the answer choices be your guide. If they are very close together, then you will need to be more accurate in your approximation. However, if the answer choices are markedly far apart, then by all means round to the nearest integer. Let’s look at a more challenging question:
In the table to the left, the amount of hardcover and paperback copies sold in a given year for novels L, M, N, P, and Q is provided. For which novel is the ratio of hardcover copies sold to the paperback copies sold the greatest for that year?
To solve this question it is MUCH faster to approximate by rounding each number to make the comparison easier. L is 800,000/1,300,000, or 8/13. Following the same logic of approximating and estimation: M is 3/6. N is 8/10. P is 3/7. Q is 10/25.
The question asks for the greatest ratio. Notice how 3/6, 3/7 and 10/25 are all around 50% or less. That leaves only 8/13 and 8/10. When the numerator stays the same and the denominator shrinks, we know we are getting a larger fraction of the total. Therefore, 8/10 is greater, so the answer is Title N.
For more practice looking at questions where Approximation & Estimation is an appropriate strategy, click on “Create Game” in the Grockit ACT lobby and make a custom game using only the skill tag “Approximation & Estimation.”
Find 2011 and 2012 ACT test dates here!
