BACKSOLVING
All of the answers in the Math Section of the SHSAT are multiple-choice. One way that you will be able to use this to your
advantage is by backsolving. What this means is that sometimes it’s helpful to work backwards from the answer choices.
Here’s how it works. When answer choices are numbers—i.e., not variables—you can expect them to be arranged from small to
large or large to small. The test maker does not get creative with the order of the answer choices. What you do is to start with the
middle answer choice and plug it directly into the problem. If it works, you’re set. If it doesn’t, you can usually figure out whether to
try a larger or smaller answer choice. If this seems confusing, take a look at the following problem and explanation.
REMEMBER
You can backsolve only if your answer choices are all numbers.EXAMPLE
Begin with the middle answer choice. If 100 is the greatest of the three numbers, the three numbers must be 100, 80, and 60. We
know that 100 + 80 + 60 = 240. The correct three numbers will add up to 300, so the greatest of these numbers must be greater than
- Try answer choice (D). If 120 is the greatest, the three numbers must be 120, 100, and 80; 120 + 100 + 80 = 300. Answer (D)
is correct.
It’s worth noting that if (D) had also given you a sum less than 300, you would not have to check choice (E). Think about it. If the
numbers are arranged from small to large and the second-largest number gives you an answer that is too small, you know that the
largest number has to be correct.
TIME TIP
Always start with the middle answer choice when solving a word problem by backsolving.57. Three consecutive multiples of 20 have a sum of 300. What is the greatest of these numbers?A. 60
B. 80
C. 100
D. 120
E. 140