Basic Mathematics and Mental Ability for Job Tests: Shortcuts That Save Time

Many recruitment tests contain a short mathematics or "mental ability" section. It usually checks arithmetic, percentages, ratios, simple algebra, number series and logical reasoning. Time is the real challenge: you may have less than a minute per question. These shortcuts and habits help you solve more questions correctly.

1. Percentages

• 10% of a number is the number divided by 10. 5% is half of that. 15% is 10% plus 5%.
• Percentage change = (change / original) × 100.
• If a price rises by 20% and then falls by 20%, it does not return to the original: it ends 4% lower.

2. Ratio and proportion

To divide a quantity in the ratio a : b, add the parts (a + b), divide the quantity by the sum, and multiply by each part. Example: divide 1,200 in the ratio 3 : 5. Sum = 8; one part = 150; the shares are 450 and 750.

3. Average

Average = total ÷ number of items. If the average of 5 numbers is 20, their total is 100. When one number is added, use totals, not averages, to find the new value.

4. Profit and loss

• Profit = selling price − cost price.
• Profit % = (profit / cost price) × 100, always on the cost price.
• Selling price = cost price × (100 + profit%) / 100.

5. Time, speed, distance

Speed = distance / time. To change km/h to m/s, multiply by 5/18; to change m/s to km/h, multiply by 18/5. For two trains moving in opposite directions, add the speeds; in the same direction, subtract them.

6. Algebra basics

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a − b)(a + b)

7. Number series and reasoning

Look for a pattern in this order: constant difference (2, 5, 8, 11), constant multiple (3, 6, 12, 24), squares or cubes (1, 4, 9, 16), alternating patterns, and increasing differences (1, 2, 4, 7, 11). For analogies and odd-one-out, first decide the relationship in a short sentence, and then test each option against it.

Exam-hall habits

1. Do the easy questions first and mark the long ones to return to.
2. Use the options: sometimes testing the options in the equation is faster than solving it.
3. Estimate first. If the answer must be near 50, an option of 500 is wrong.
4. Check units (minutes vs hours, rupees vs paisa).

How to practise

Spend 30 minutes a day: 10 minutes on revising formulas, 20 minutes on timed questions. Set a limit of 45 seconds per question. Keep a "formula page" on the wall near your study table and read it every morning.