Basic Mathematics and Reasoning
Basic Mathematics and Reasoning here is speed arithmetic: percentages, ratio, average, simple and compound interest, time-speed-distance, plus series, coding-decoding, blood relations and direction sense. No calculators are allowed, so answers are whole numbers or simple fractions.
Core rules
- BODMAS: brackets, orders, division and multiplication left to right, then addition and subtraction left to right.
- Percentage change = (change / original) x 100. A 20% rise followed by a 20% fall leaves 96% of the original, not 100%.
- Two successive discounts of a% and b% equal a + b - ab/100, not a + b.
- Average = sum / count; adding a value equal to the average leaves it unchanged.
- SI = P x R x T / 100; CI = P(1 + R/100)^T - P.
- km/h to m/s: multiply by 5/18.
Worked example
An article marked Rs 1,200 gets successive discounts of 10% and 5%. First discount: 1,200 - 120 = Rs 1,080. The second discount applies to Rs 1,080: 5% of 1,080 = Rs 54, so the selling price is Rs 1,026. Check with the formula: 10 + 5 - (10 x 5)/100 = 14.5% total, and 1,200 x 0.855 = Rs 1,026. Both routes agreeing is your verification.
Reasoning pattern
Series 3, 7, 15, 31, ? Each term is double the previous plus one, so the next is 63. Test difference, ratio and square patterns before guessing.
Traps
Adding successive discounts; using the simple-interest formula for two years of CI; taking the new value as the base for a percentage change; ignoring the left-to-right rule inside BODMAS.