This week, we are solving another tricky problem from The Real ACT Prep Guide, aka the “Red Book.” This time it is the Science section we are targeting–specifically Test 2, Question 13 on page 332.
This is a question that unsettles a lot of students because it involves a little bit of math. Most of the time on the Science test, you are just going to be looking up numbers on the tables and figures. But there are a few questions on each test that will require you to do some simple math. Sometimes this might mean converting to scientific notation, sometimes it might mean deriving a proportion from data on the graph, sometimes it might mean translating percent values into numbers.
You will need to follow along in the Red Book for the complete passage and figures for this problem, but we will work through the question below (you can also check out the explanation video above for the relevant table!)
13. Based on the results of Activity 2, the combination of which of the following lines and objective lenses would result in the greatest image size?
- A 0.7 mm line viewed through Objective Lens 1
- A 0.6 mm line viewed through Objective Lens 2
- A 0.5 mm line viewed through Objective Lens 3
- A 0.4 mm line viewed through Objective Lens 4
Table 2 gives us the various objective lenses and their magnification. But we need to look at the passage right above the table in order to figure out how the line lengths in the question tie into the passage. The passage tells us that for Activity 2, the student was given a prepared slide with a line on it that was 0.1 mm in length. But the answer choices in our question switches this variable up and asks us to consider longer lines.
The passage also tells us that the magnification number (M) is calculated by dividing the image size by the object size (M = image size / object size).
So if, as Table 2 tells us, Objective Lens 1 has a magnification of 40 and an image size of 4 this translates to:
40 = 4 / 0.1
The magnification of each respective objective lens does not change. But if we change the original object size, as the answer choices do, then the image size is going to change.
So our equation for answer choice A would look like this:
40 = x / 0.7
(plugging in 0.7 mm from the question and knowing M = 40 for Objective Lens 1)
answer choice B:
100 = x / 0.6
answer choice C:
200 = x / 0.5
answer choice D:
400 = x / 0.4
So we COULD do the math here, but wait a second! This isn’t terribly hard math, but it is not terribly easy either: this isn’t the Math test, and the Science test doesn’t expect that much of you. Let’s take a look and see if we can figure it out without actually doing the math.
The value for the original object line does not change all that much between the answer choices (it only varies between 0.4 mm and 0.7 mm) but the magnification is changing a LOT.
We have a magnification value in answer choice D that is much larger than in answer choice A. So if we multiply 400 by a number that is only 0.3 away from the number we are multiplying 40 by in answer choice A, it stands to reason that D is going to give us the largest answer, meaning the greatest image size, and, in fact, D is our answer. (You can do the math if you are still skeptical 🙂 ).
So, remember, on the ACT Science, don’t be caught off guard if you are asked to do some math, but don’t forget that it shouldn’t be very difficult math, either. If you feel like that is the case, look for how you can reason out the answer. That’s what the Science test is hoping to measure anyway!