Malik earns $10 per hour

2026 Practice Tests (digital)

2026 Practice Test C Math · Question 45 of 50

Question

Malik earns $10 per hour at his job. He wants to change to a job that will pay $12 per hour. What will be the percent increase in Malik’s hourly pay if he makes this job change?

A2%
B20%
C83%
D120%

Show the answer

Correct answer: B

Subtract to determine the amount of increase in Malik’s hourly pay if he changes jobs.

$12 - 10 = 2$

Divide the increase amount by the original hourly pay rate.

$2 \div 10 = 0.2$

Multiply the quotient by 100 to express the decimal amount as a percentage.

$0.2 \times 100 = 20$

Question analysis

Malik earns $10 an hour and wants to switch to a job that pays $12 an hour. Students find the percent increase in his hourly pay. It tests finding a percent change. The numbers are easy, so the challenge is knowing which amounts to compare and how to turn that comparison into a percent.

NYS standards: 7.RP.3 multistep ratio and percent problems
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: At grade 7 Percent increase is grade 7 content, and this case uses whole-dollar wages that make the arithmetic easy. The demand is comparing the change with the right amount rather than reporting the change itself or a ratio of the wages.
Estimated difficulty: Straightforward: two steps or one careful reading.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Something you must already know minor
Turning words into math minor
Solution: 2 steps
Reading level: Question and choices: about grade 2, 35 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The numbers could hardly be friendlier, a $2 raise on $10, so the question checks what to divide by what. Dividing $12 by $10 gives 1.2, the new pay as a percent of the old, and stopping there is tempting because the division feels like the whole job. Reading the $2 itself as 2% is the other quick error, since dollars of change are not percent of change.

Something you must already know minor Working it out
The rule for percent change, the change divided by the starting amount, is not given, and each wrong choice comes from a different comparison of the $10 and the $12. (Anderson & Krathwohl, 2001)
Turning words into math minor Understanding the question
“Percent increase in Malik’s hourly pay” has to be read as the $2 rise measured against the $10 he earns now, not as the new wage compared with the old. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

Strategy: Find how many dollars the hourly pay goes up, then divide that change by the pay Malik earns now and write the result as a percent.

Traps

Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).

The wrong answers, classified

A Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Reveals a misconception Expected pull: moderate
Finds the $2 increase and reads it as 2%, as if a change in dollars were a percent, without dividing it by the original $10.
C Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Reveals a misconception Expected pull: weak
Divides the old pay by the new, 10 ÷ 12 ≈ 0.83, turning the ratio of the wages upside down and reporting 83%.
D Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals partial knowledge Expected pull: strong
Divides the new pay by the old, 12 ÷ 10 = 1.2, which gives the new wage as a percent of the old, not the increase.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent increase: $\text{percent increase} = \frac{\text{new} - \text{original}}{\text{original}} \times 100$; The original is the amount before the change. The new amount is the amount after it. The top is how much it went up. Dividing by the original compares the change with where you started. Multiplying by 100 makes it a percent.

Sort out the question
Malik earns $10 an hour now. The new job pays $12 an hour. You need the percent increase.
That means: how much does his pay go up, compared with what he earns now? So $10 is the original amount, and $12 is the new amount.
Find the increase in dollars
Subtract the old pay from the new pay:
$12 - 10 = 2$
His pay goes up by $2 an hour.
Watch out: $2 is an amount of money, not a percent. Calling it 2% gives choice A.
Compare the increase with the original
Use the percent increase formula. Divide the $2 by the original $10, then multiply by 100:
$\frac{2}{10} \times 100 = 0.2 \times 100 = 20$
So the pay goes up by 20%.
Watch out: $12 \div 10 = 1.2$ is 120%, choice D. That is the new pay as a percent of the old, not the increase. And $10 \div 12$ is about 83%, choice C, which is upside down.
Give the answer
The $2 raise is 20% of Malik’s current pay.
So the answer is B, 20%.

Check your answer

Work forward. 20% of $10 is $0.20 \times 10 = 2$ dollars. Add that to $10, and you get $12, the new pay. It works. Note that 120% is the new pay compared with the old pay, which is the same as a 20% increase.

The original DOE question

Question 45 as shown on the DOE’s digital test, page 118 of its printable version. — As printed in the DOE’s printable version of 2026 Practice Test C Math, page 118, question 45.