SHSAT Sunset

The price of a sandwich was raised

2024 Handbook

2024 Test A Math · Question 40 of 57

Question

The price of a sandwich was raised from $6.25 to $6.75. What was the percent increase in the price?

  • A5%
  • B8%
  • C7%
  • D50%
Show the answer

Correct answer: B

Use the percent increase expression to find the answer:

new price−original priceoriginal price\frac{\text{new price} - \text{original price}}{\text{original price}}

6.75−6.256.25=0.506.25=0.08=8%\frac{6.75 - 6.25}{6.25} = \frac{0.50}{6.25} = 0.08 = 8\%

Question analysis

A sandwich's price went up from $6.25 to $6.75, and this percent change question asks for the percent increase in the price. Students divide the 50-cent increase by one of the prices and write the result as a percent. Picking which price is the base, and doing the decimal division accurately, decide whether the answer comes out right.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 6.NS.3 multi-digit decimal operations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
At grade 7 Finding a percent increase is a core grade 7 skill, and this is the plain version with no context beyond two prices. Its demand lies in measuring the change against the correct price and dividing by $6.25 without a calculator.
Estimated difficulty
Moderate: several steps, or a close reading with one strong distractor.
What makes it hard
Solution
3 steps
Reading level
Question and choices: about grade 2, 17 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 50-cent rise is easy to find; the percent depends on what it is compared with. Dividing by the new price, $6.75, gives a value that rounds to a listed choice one point below the answer, and reading 50 cents as 50 percent gives another. The choices are printed out of order, 8% before 7%, so students should read each one rather than scan the list.

  1. A very close wrong answer moderate Choosing the answer

    Measured against $6.75 the 50-cent rise is about 7.4%, and against $6.25 it is 8%; both are listed side by side, so only the right base separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  2. Error-prone arithmetic moderate Working it out

    The division 0.50 ÷ 6.25 is easiest as 50/625, which reduces to 2/25 and then to 8/100; a three-digit decimal divisor invites a slip. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Put the 50-cent change over the original price, 0.50 over 6.25, then scale the fraction to hundredths or divide to read off the percent.

Traps

  • Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
  • 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.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent increase
percent increase=new−originaloriginal×100\text{percent increase} = \frac{\text{new} - \text{original}}{\text{original}} \times 100
New is the price after the change, and original is the price before it. The top is the amount of the increase. Dividing by the original compares the increase with where you started. Multiplying by 100 turns that decimal into a percent.

  1. Sort out the question

    The sandwich cost $6.25 before. That is the original price. Now it costs $6.75, the new price. You need the percent increase. That compares the increase with the original price. Note that the choices are not in order: C, 7%, comes after B, 8%.

  2. Find the amount of the increase

    6.75−6.25=0.506.75 - 6.25 = 0.50

    The price went up $0.50, or 50 cents. Watch out: 50 cents is not 50%. It would be 50% only if the price started at $1.00. That mistake gives choice D.

  3. Divide by the original price

    percent increase=new−originaloriginal×100\text{percent increase} = \frac{\text{new} - \text{original}}{\text{original}} \times 100

    6.75−6.256.25×100=0.506.25×100\frac{6.75 - 6.25}{6.25} \times 100 = \frac{0.50}{6.25} \times 100

    In cents, this is 50 out of 625. Divide the top and bottom by 25. Then multiply both by 4 to get hundredths.

    50625=225=8100=0.08\frac{50}{625} = \frac{2}{25} = \frac{8}{100} = 0.08

  4. Change to a percent

    0.08×100=80.08 \times 100 = 8

    The price went up 8%. Watch out: divide by the original price, $6.25, not the new one. Dividing by $6.75 gives about 7.4%, which is choice C.

    So the answer is B, 8%.

Check your answer

Work forward from the answer. 8% of $6.25 is 0.08×6.25=0.500.08 \times 6.25 = 0.50, or 50 cents. Then 6.25+0.50=6.756.25 + 0.50 = 6.75. That is the new price, so 8% is right.

More questions like this

The original DOE question

Question 97 as printed on page 86 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 86, question 97. Open page 86 of the handbook (PDF)