Because the answer choices are provided, multiple-choice questions offer alternative, Back-Door strategies for determining the correct answer choice. These Back-Door strategies are Elimination, Backsolving, and Pick a Number.
ELIMINATION
Often one or more answer choice can quickly be eliminated just by applying a little reasoning or common sense. Eliminating even one incorrect answer choice greatly improves the student's chances of getting the correct answer.
Using Elimination
The ratio of men to women at a party is exactly 3:2. If there are a total of 120 people at the party, how many of them are women?
A. 36
B. 48
C. 72
D. 80
- Which answer choices can be quickly eliminated? Why?
- What strategy can now be used on the remaining answer choices?
Tips for Elimination
- Eliminate choices that are too extreme.
- Eliminate choices that contradict the facts.
- Eliminate choices that attempt to lure you with the obvious.
Improve Your Odds
Students will always benefit from eliminating wrong answer choices as soon as they spot them.
BACKSOLVING
Backsolving means working backwards by plugging the numbers from each answer choice back into the problem until the correct answer is found.
Using Backsolving
Martin printed invitations to his party at a local printer. The printer charges $2.50 for the first 20 copies, and $0.10 for each additional copy. If Martin paid $8.70 and there was not tax, how many copies did Martin make?
A. 62
B. 67
C. 77
D. 82
- Why is it best to choose the number for answer choice B or C to begin backsolving?
Tips for Backsolving
Backsolving works best when:
- the question is a complex word problem and the answer choices are numbers.
- the alternative is setting up multiple algebraic equations.
Don't backsolve if:
- the answer choices contain variables.
- the answer choices are radicals, fractions, irrational numbers, or other values that would take too much time to plug in.
The Easy Way
For many word problems, Backsolving may be easier than translating the problem into algebra.
PICK A NUMBER
If there are variables in the answer choices, students should consider using the Pick a Number strategy. Here's how it works:
- Pick numbers for each of the variables.
- Plug the numbers into the question and find the result.
- Next, substitute the numbers for the variables in each answer choice.
- Now simplify each answer choice and compare the results to the original value.
Using Pick a Number
If s skirts cost d dollars, how much would s - 1 skirts cost?
A.
d - 1
B.
d - s
C.
d /
s - 1
D.
d(
s - 1) /
s
- What numbers did you select to represent the two variables?
- Using these values, how much would s - 1 skirts cost?
- Which answer choice matches this cost?
Tips for Picking a Number
- Pick small numbers that are easy to work with.
- When there are two variables, pick different numbers for each.
- Avoid picking 0 or 1, as these often give several "possibly correct" answers.
Plug carefully
When plugging values in for variables, make sure you are using the right number for each variable.
