Handle cases where the percent is greater than 100%. | Percentages | SAT Math

核心知识

A percent greater than 100% simply means more than the whole. 150% of a number means 1.5 times that number. The same conversion rules apply — nothing special changes.

深入理解

Students sometimes freeze when they see a percent above 100, but the mechanics are identical. 250% just means $250100 = 2.5$ . If your salary is 250% of what it was five years ago, you earn 2.5 times your old salary.

The trickier phrasing is percent increase versus percent of. "A 150% increase" is not the same as "150% of the original." A 150% increase means the new value is the original plus 150% of it:

N e w = O r i g i n a l \times (1 + 1.50) = O r i g i n a l \times 2.50

So a 150% increase gives you 250% of the original.

This distinction is the most tested trap in percent-greater-than-100 problems. The SAT will use language designed to make you confuse the two.

Another common setup: "The number of members this year is 340% of last year's." That means multiply by 3.40 — the increase itself was 240%, but the total is 340% of the base.

When you see a large percent, convert to a decimal immediately and ask: does the problem say "percent of" or "percent increase"? That one question will keep you out of trouble.

分步讲解

Convert the percent to a decimal, even if it's above 1.0 (e.g., 175% = 1.75).
Determine whether the problem says 'percent of' (multiply directly) or 'percent increase' (use 1 + r as the multiplier).
Calculate: for 'X% of Y,' compute $𝑋 100 \times 𝑌$ . For 'X% increase,' compute $𝑌 \times (1 + 𝑋 100)$ .
Sanity-check: the result should be larger than the original. If it's smaller, re-read the problem.

常见误解

Confusing 'a 200% increase' with '200% of the original' — a 200% increase triples the value $(\times 3)$ , while 200% of the original doubles it $(\times 2)$ .
Assuming percents can't exceed 100 and capping calculations at the original value.
Subtracting 100 from the percent before multiplying when the problem says 'percent of' rather than 'percent increase.'

题目

示例解析

A company's revenue in 2023 was $400,000. In 2024, revenue was 175% of the 2023 revenue. What was the revenue increase from 2023 to 2024?

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