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SSAT MIDDLE LEVEL • QUANTITATIVE

Solve problems involving percent increase or decrease.

Master how values grow or shrink by percentages, like game scores or store sales.

SECTION 1

Historical Context & Motivation

Long ago, people needed a way to talk about changes in amounts, like more crops or fewer coins. Percents come from the Latin words "per centum," meaning "by the hundred." They help us see how much something changes compared to before. Think of it like tracking points in a soccer game.

15th Century
Birth of Percents
Italian merchants used percents for trade deals and profits.
1700s
Taxes and Growth
Governments tracked tax increases with percents.
1900s
Everyday Use
Schools taught percent change for sales and sports stats.
Today
Test Prep
SSAT uses it to build your math superpowers!

Before percents, changes were hard to compare. Now, you can quickly see if your video game high score jumped by 20%. This solves real-world puzzles like price tags or team wins.

SECTION 2

Core Principles & Definitions

A percent increase happens when a value grows bigger. Percent decrease is when it gets smaller. Both compare the change to the original amount.

1

Original Value

The starting amount, like 100 points in a game.
2

Change Amount

New minus original, like +20 points.
3

Percent Change

(Change / original) × 100%. Always out of 100!
4

Increase vs Decrease

Positive for growth, negative for shrink.
⚽ Quick Tip
Imagine your soccer team's score goes from 5 to 7 goals. That's a 40% increase! Like leveling up in a game—small changes add up big.
SECTION 3

Visual Explanation

The blue bar shows the original $10 price. The cyan bar is taller for the new $12 price. The difference is 20% of original.

See how the new bar is taller? That's growth! The diagram makes it easy to spot percent increase visually, like comparing candy bar sizes before and after a sale.

SECTION 4

Mathematical Framework

The math is simple. Find the change, divide by original, then multiply by 100 for percent. Always use the original as the bottom number!

PERCENT CHANGE
((new − original) / original) × 100%
If new > original, it's increase. If new < original, decrease. original ≠ 0.
MULTIPLIER
new = original × (1 ± (percent / 100))
+ for increase, − for decrease. Great for checking work!

Plug in numbers step by step. You'll feel like a math wizard on the SSAT!

SECTION 5

Detailed Breakdown

Increase and decrease work the same way but flip the sign. Watch for words like "rose by" or "dropped."

Circle starts at 100. Green arrow up to 120 (+20%). Red arrow down to 80 (−20%). Same percent, different results.

The diagram shows both paths from the same start. Up for more, down for less—like jumping higher or sinking in a game.

SECTION 6

Worked Example

Candy Price Jump
1
Step 1 — Find ChangeOriginal: 50¢, New: 60¢. Change = 60 − 50 = 10¢
10¢
2
Step 2 — Divide by Original10 / 50 = 0.2
0.2
3
Step 3 — To Percent0.2 × 100 = 20% increase!
20%

See? Easy steps. Practice this, and SSAT problems will seem like fun challenges.

SECTION 7

Strengths & Common Mistakes

Spot traps to boost your score!
Do ThisAvoid This
Use original as denominator.Don't use new value.
Check if increase or decrease.Forget the sign.
Multiply by 100 last.Skip ×100%.
🛑 KEY TAKEAWAY
Percents shine for quick comparisons, like sale prices. But always double-check the base—like aiming before kicking the ball.
SECTION 8

Connections to Advanced Ideas

Basic Percent ChangeAdvanced (Compound)
One-time change.Change over time, like interest.
Simple formula.(1 + r/100)^n.

Master basics now, and compound growth is next—like daily training making you a sports star. SSAT preps you perfectly!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL
What does a 0% increase mean? A) Value halves B) Value doubles C) No change D) Value triples E) Value disappears
PROBLEM 2 — BASIC CALCULATION
A shirt costs $20, now $25. Percent increase? A) 10% B) 20% C) 25% D) 30% E) 50%
PROBLEM 3 — INTERMEDIATE
Team score: 40 to 32. Percent decrease? A) 10% B) 20% C) 25% D) 30% E) 40%
PROBLEM 4 — APPLIED
Game level 50 gems to 65. Increase? A) 15% B) 25% C) 30% D) 50% E) 65%
PROBLEM 5 — CRITICAL THINKING
Price drops from 80¢ to 64¢, then up 25%. Final percent from original? A) −10% B) 0% C) +10% D) −20% E) +20%
SUMMARY

Lesson Summary

You can now crush percent increase/decrease! Use ((new−original)/original)×100%. Check original base.

Practice builds speed for SSAT. You're ready—go get those top scores! 🚀

Varsity Tutors • SSAT Middle Level • Solve problems involving percent increase or decrease.