GRE Percentages
Percentages show up all over the GRE, from data interpretation to word problems. The arithmetic is easy; the points are lost on wording and on one specific trap with percent change. Here is everything that actually comes up.
Percent of: just multiply
A percent is a number over 100. To take “x percent of N,” multiply N by x/100. So 35% of 80 is 80 x 0.35 = 28. Convert fluently between percent, decimal, and fraction, and memorize the common conversions so you are not doing long division under time pressure:
- 1/2 = 50%, 1/3 is about 33.3%, 2/3 is about 66.7%
- 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/8 = 12.5%
- To go percent to decimal, move the point two places left: 7.5% = 0.075.
Percent change, and the trap
Percent change = (new - old) / old x 100, always divided by the original amount. An increase uses a multiplier above 1 (up 20% means x 1.20); a decrease uses one below 1 (down 20% means x 0.80).
The trap: successive percent changes multiply, they do not add. Up 20% then down 20% is 1.20 x 0.80 = 0.96, a net 4% decrease, not zero. The GRE loves this exact setup, and “it is back to the start” is always a wrong answer.
Read the wording: of vs. greater than
“A is 20% of B” means A = 0.20B. “A is 20% greater than B” means A = 1.20B. “A is 20% less than B” means A = 0.80B. The word “of” is a direct multiply; “greater than” or “less than” adjusts from 100%. Misreading this is a far more common error than any calculation.
Reverse percents
When you are given the amount after a change and asked for the original, divide by the leftover fraction, do not re-apply the percent. If a price is $60 after 25% off, then $60 is 75% of the original, so the original is 60 / 0.75 = $80. Adding 25% to $60 gives $75, which is wrong, and it is a planted answer choice.
Frequently asked questions
If a price goes up 20% then down 20%, is it back to the start?
No. Successive percent changes multiply, they do not add. Up 20% then down 20% is 1.20 x 0.80 = 0.96, so you end 4% below where you started. This is the single most common GRE percent trap.
How do I turn a percent into something I can compute with?
Divide by 100 to get a decimal (35% = 0.35) or use a known fraction. Memorize the common ones: 1/2 = 50%, 1/3 is about 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%. 'x percent of N' is always N times x/100.
What is the difference between 'percent of' and 'percent greater than'?
'A is 20% of B' means A = 0.20B. 'A is 20% greater than B' means A = 1.20B. Watch the wording: 'of' is a straight multiply, 'greater/less than' adds or subtracts from the original 100%.
A shirt is $60 after 25% off. What was the original price?
Do not add 25% back. $60 is 75% of the original, so original = 60 / 0.75 = $80. Reverse-percent questions are solved by dividing by the leftover fraction, not by applying the percent again.
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More GRE Quant: all topics, formula sheet.