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This essential trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 5-6, Math Kangaroo 7-8.

Summary

Assume a quantity Q.

 A percentage p of Q is: Example: "3 percent of 65":  A percentage p less than Q is: Example: "3 percent less than 65":  A percentage p more than Q is: Example: "3 percent more than 65":  Typical Questions

How much is 3% of 65? How much percent of 65 is 1.95?  1.95 is 3% of what number?  How large does a quantity become if it increases by p percent?

If the initial value of the quantity is Q, then the final value is: Using Q=65 and p=3% as numerical values, the shortest way to compute the final value is: How small does Q become if it decreases by p percent?

If the initial value of the quantity is Q, then the final value is: Using Q=65 and p=3% as numerical values, the shortest way to compute the final value is: How much percent of Q is another quantity R?  Numerically, how much percent of 65 are three fifths of 65:  The answer is 60%. How does this differ from: Obviously, What is the final value of Q after an increase of 30%, followed by a decrease of 75%, followed by an increase of 28%?

For each change, we have to use as initial value the final value of the previous change: The final value is 41.6% of the initial value.

By how much percent has the quantity decreased?

When combined, these changes amount to a decrease of 58.4%: If Q increased by another quantity q, what is the percentage it increased by?  Numerically, if Q is 65 and q is 1.95: Q has increased by 3%.

If Q changes from an initial value to a final value what is the percent increase or decrease? The sign of the result will tell you if it is an increase or a decrease.