3 Strategies to Tackling Multiple Choice questions

1. Plug in a number

2. Back-solving

3. Guessing

Tackling Multiple Choice Questions1. Plug in/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.

Plug in/Pick a numberUsing Pick a Number

If s skirts cost d dollars, how much would s - 1 skirts cost?

A. d - 1B. d - sC. d / s - 1D. 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?

Plug in/Pick a numberTips 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.

PRACTICE: Plug in/Pick a number

Explanation: Plug in/Pick a number

PRACTICE: Plug in/Pick a number

Explanation: Plug in/Pick a number

Tackling Multiple Choice Questions2. Back-solving– Use when picking numbers and solving the

problem isn’t possible– Work back-wards using answer choices

Back-solving• How to back-solve– Plug choices back into the question until you find

the one that fits– Answer choices are arranged in order, either

descending or ascending from (A) to (E)– Choose choice (C) first to plug into the equation to

guide your next step • If it gives you too small an answer, then (A) and (B) or (D)

and (E) can be eliminated depending on which values are smaller than (C)

Back-solving• When to back-solve– Question is a complex word problem & answer

choices are numbers– The alternative is to set up multiple algebraic

equations• When back-solving isn’t ideal– Answer choices include variables– Algebra quest. And word problems that have ugly

answer choices (radicals, fractions)

Practice with Back-Solving

Practice with Back-Solving

Tackling Multiple Choice Questions3. Guessing– Avoid random guessing– Make educated guesses– Eliminate unreasonable answer choices– Eliminate the obvious answers on hard

questions– Eyeball lengths, angles, and areas on

geometry questions

Guessing

• Eliminate unreasonable answer choices– Which answers don’t make sense

• Eliminate the obvious on hard questions– Obvious answers are usually wrong for hard

questions– Don’t use this for easy questions, the obvious

answer might be right

Guessing• Eyeballing lengths, angles, & areas– Use diagrams to help you eliminate wrong

answer choices– Double check to see if the diagram is drawn to

scale• If it’s not drawn to scale, you can’t use this

strategy—figures are drawn to scale unless otherwise noted• If it is, estimate quantities or eyeball the diagram,

angle, length, or area

Guessing• Eyeballing lengths, angles, & areas– eliminate answer choices that are too large or

too small– With angles, compare them to 180°, 90°, or

45° angles • Use the corner of a piece of paper (right angle) to

see if an angle is > or < 90°– With areas, compare an unknown area to an

area that you do know

PRACTICE GUESSING

Grid-In Questions

• No answer choices• 4 boxes and a column of ovals, or bubbles to

write your answer• No penalty for wrong answers

Grid-In Questions

• Some questions have only 1 correct answer, others have several

• Digits, decimal points, fraction signs should be written in separate boxes

• Bubble in underneath

Grid-In Questions

• You can’t grid– Negative numbers– Answers with variables– Answers greater than 9,999– Answers with commas (1000 not 1,000)– Mixed numbers (ex: 2 ½)

Grid-In Strategies• Write (.7 not 0.7)• Grid fractions in the correct column– Ex: 31/42 won’t fit & will need to be converted into

a decimal• Place decimal points carefully– If decimal <1, enter the decimal point in the 1st

column (.127)– Only grid in a 0 before the decimal if it is part of the

answer (20.5)– Never grid a decimal point in the last column

Grid-In Strategies• Long or repeating decimals– Grid the first 3 digits only and plug in the

decimal point– Rounding to an even shorter answer may be

incorrect – try not to round• If there is more than 1 right answer,

choose 1 and enter it

Grid-In Strategies• If the answer has a range of possible

answers, grid any value between that range– It’s easier to work with decimals– Ex: 1/3 < m < ½ • Don’t grid 1/3 or ½ -- that would be wrong• Grid .4 or .35 or .45

• Check your work

Using Calculators

• Help the most on Grid-ins• Use it only to save time• If you can’t think of a reason why using a

calculator would make a problem easier or quicker to solve, don’t use it

Using Calculators1. Think first2. Decide on the best way to solve the

problem3. Only then, use your calculator4. Check your answers• Be sure that calculations involving parenthesis

are correct before pressing “enter”• Don’t forget PEMDAS– Parenthesis, exponent, multiply, divide, add, subtract

GRID IN PRACTICE 1

There are 12 men and 24 women in a chorus. What percent of the entire chorus is composed of women? (Disregard the percent sign when gridding your answer).

12+ 24= 3624/36= 66.66666666

66.6 OR 66.7

GRID IN PRACTICE 2

Note: figure not drawn to scale

If x and y are integers and x > 90, what is the minimum possible value of x ?

One way to reason through this problem is as follows. The interior angles of a triangle add up to 180 . So� x + y + 3y = 180, or x + 4y = 180. Try the smallest

integer value of x greater than 90 in this formula, that is, x = 91. This gives , so . Thus if x = 91, . But y must be an integer, so x must be a larger number. Try the

next greater integer value for x. If x = 92, then , so , which means that . Since y is an integer in this case, the minimum value of x is 92.

92

GRID IN PRACTICE 3A gumball machine dispenses gumballs of different colors in the following pattern: green, blue, red, red, yellow, white, white, green, and green. Assuming the pattern repeats itself, if the machine dispenses 60 gumballs, how many of them will be green?

This is a classic pattern question—with a twist. The key here is to count the number of elements in the given pattern. This pattern has 9

elements that repeat. Of these, three are green. So every time the machine goes through the pattern, 3 of the gumballs it dispenses are

green. 60 is not a multiple of 9, but 54 is. When the machine is up to the 54th gumball, it will have gone through this pattern of 9 exactly 6 times. So it will have dispensed green gumballs. For the remaining 6, just count

into the pattern. Only one more green gumball will be dispensed 19