Rapid Revision · Quantitative Aptitude
Percentages power half of quant: profit and loss, interest, data interpretation. Master the multiplying factor and everything else gets faster.
If you read nothing else tonight, read these 6 lines.
Every formula for percentages in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
x percent of N
x% of N = (x / 100) x N
Percentage change
change% = (change / original) x 100
Divide by the ORIGINAL value, never the new one.
Successive changes
net% = a + b + (a x b) / 100
Minus sign for a decrease; chains any two back-to-back changes.
Multiplying factor
+x% -> x (1 + x/100) -x% -> x (1 - x/100)
More / less reversal
A is x% more than B => B is (x / (100 + x)) x 100 % less than A
Compound growth
final = P x (1 + r/100)^n
n periods of r% growth: population, price, CI principal.
8 cards, each one idea: what it is, a worked example, and the trap to dodge.
Memorize: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%, 1/12 = 8.33%. Converting to fractions turns arithmetic into cancellation.
37.5% of 64 = (3/8) x 64 = 24.
Trap: Do not mix up 1/6 (16.67%) with 1/8 (12.5%) under time pressure.
change% = (new - old) / old x 100. The denominator is always the original value.
40 to 50: 10/40 = 25% increase. But 50 to 40 is 10/50 = 20% decrease.
Trap: A 25% rise is NOT undone by a 25% fall; the base has changed.
Two changes a% then b%: net% = a + b + ab/100. Decreases go in as negatives.
+20% then -10%: 20 - 10 - 2 = +8%.
Trap: Do not just add the percentages; the ab/100 term is where marks are lost.
+15% is x1.15, -20% is x0.80. Chain factors for multiple changes instead of computing step by step.
240 raised 25% then cut 10%: 240 x 1.25 x 0.9 = 270.
If A is x% more than B, then B is x/(100+x) x 100 % less than A. If A is x% less, B is x/(100-x) x 100 % more.
A is 25% more than B: B is 25/125 x 100 = 20% less than A.
Trap: The two percentages are never equal; swapping them is the classic error.
Price rises x% and spending stays fixed: cut consumption by x/(100+x) x 100 %.
Price +25%: reduce consumption by 25/125 x 100 = 20%.
After n periods at r% per period: P x (1 + r/100)^n for growth, P x (1 - r/100)^n for depreciation.
10000 at 10% for 2 years: 10000 x 1.1 x 1.1 = 12100.
Trap: This is compound behavior; do not use the simple-interest style P(1 + nr/100).
20% to 25% is a rise of 5 percentage points, but a 25% relative increase (5/20). Tests love this wording.
Interest rate from 8% to 10%: +2 points, +25% relative.
A recap is not practice. These are the creators we rate for real depth on percentages; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.