Percentages Pattern - Data Extraction

Pulling the right numbers from a word problem or data table before doing a percentage calculation

These questions pair a table or data-heavy word problem with a percentage calculation. The math itself is straightforward — the challenge is finding the correct pair of numbers in the data before you compute.

The Core Skill

You're given a table with several rows and columns (or a word problem with lots of numbers). The question says something like "A is $p\%$ of B." You need to:

1. Identify A and B in the data.
2. Set up the equation: $A = \dfrac{p}{100} \times B$
3. Solve for the unknown (usually $p$).

Example — Table with Multiple Rows

The table shows the number of students in four departments at a university. The number of students in Arts is $p\%$ of the number of students in Science. What is $p$?

Department	Students
Science	450
Arts	720
Engineering	500
Business	830
Total	2,500

The question says "Arts is $p\%$ of Science."
$720 = \dfrac{p}{100} \times 450$
$p = \dfrac{720}{450} \times 100 = 1.6 \times 100 = 160$
Answer: 160

Common Traps

• Using the total instead of the specific category. If the question asks "$p\%$ of Science," the denominator is 450 (Science), NOT 2,500 (Total). The total row is a distractor.

• Swapping numerator and denominator. "Arts is $p\%$ of Science" means Arts goes on top and Science goes on the bottom: $\dfrac{720}{450}$. Flipping it gives $\dfrac{450}{720} \approx 62.5\%$, which is the reverse relationship.

• Reading the wrong row. With four departments listed, it's easy to grab Engineering (500) instead of Science (450). Slow down and read the specific categories named in the question.

Example — Word Problem with Large Numbers

A website received $1{,}200{,}000$ visitors in a month. Of these, $1{,}020{,}000$ accessed the site using a mobile device. What percentage used a mobile device?

A) 15%
B) 75%
C) 85%
D) 98%

$\text{Percent} = \dfrac{1{,}020{,}000}{1{,}200{,}000} \times 100 = 0.85 \times 100 = 85\%$
Answer: C

Gotcha — The Complement: Choice A (15%) is the percentage who did not use mobile ($100\% - 85\%$). Always confirm whether the question asks about the group or its complement.

Simplification Tip: Cancel trailing zeros before dividing: $\dfrac{1{,}020}{1{,}200} = \dfrac{102}{120} = \dfrac{17}{20} = 0.85$.

What to Do on Test Day

• Underline the two categories named in the question before looking at the table. This prevents you from grabbing the wrong row.
• "A is p% of B" → A goes on top, B on the bottom: $\dfrac{A}{B} \times 100 = p$
• Ignore the total row unless the question specifically asks about it.
• Note that $p$ can exceed 100. If Arts has more students than Science, $p > 100$. Don't be alarmed by answers like 160% — they're valid.
• Simplify large numbers by canceling common factors or trailing zeros before dividing.