tags: - cocubes - aptitude - quant - methods

Quant Methods

1. Percentage questions: use a base of 100

If no actual value is needed, assume the original quantity is 100.

Example: A salary rises by 25% and then falls by 20%.

Start: 100.
After rise: 125.
After fall: 100.
Net change: 0%.

This avoids unnecessary algebra.

2. Ratio questions: convert only when necessary

Example: A:B = 3:5 and B:C = 10:7.

Make B equal: multiply the first ratio by 2.

A:B:C = 6:10:7.

Do not add ratios unless they describe compatible quantities.

3. Average questions: think in totals

If the average of 8 values is 15, total = 120. Adding 24 gives total 144 across 9 values, so new average = 16.

The trap is averaging averages without accounting for group sizes.

4. Time and work: convert people into rates

If A does a job in 12 days, A's one-day work is 1/12. If B does it in 18 days, combined work is:

1/12 + 1/18 = 5/36.

Time required = 36/5 days.

For a worker joining or leaving, split the job into phases and calculate work done in each phase.

5. Speed questions: draw a line

For train questions, write:

distance covered = train length + object/platform length.

For same-direction meeting/overtake questions, use relative speed. For equal-distance journeys, use the harmonic-mean average-speed formula, not the ordinary average.

6. Mixture questions: track pure content

Example: A 40-litre mixture is 25% acid. Pure acid = 10 litres. If 10 litres of water is added, acid remains 10 litres and total becomes 50 litres, so concentration becomes 20%.

7. Data interpretation: estimate first, calculate second

Read the title, units and years/categories.
Mark what the question asks: difference, ratio, percentage or total.
Estimate options before detailed arithmetic.
Use exact arithmetic only if two options remain close.

Never calculate all bars/tables when the question needs only two.

8. Number system: use cycles

For the unit digit of 7^103:

Cycle length is 4: 7, 9, 3, 1.
103 mod 4 = 3.
Answer is the third element: 3.

For remainders with big powers, look for a repeating cycle modulo the divisor.

9. Probability: define the sample space

Before multiplying or adding probabilities, ask:

Are events independent?
Are outcomes equally likely?
Does order matter?

Use multiplication for "and" in independent events. Use addition for mutually exclusive "or" events. Use complement for "at least one."

Quant traps checklist

[ ] Did I use the correct base for a percentage?
[ ] Did I convert minutes/hours and km/h/m/s?
[ ] Did I use total, not average, when adding/removing members?
[ ] Did I add rates, not times, in work problems?
[ ] Did I check whether equal-distance average speed needs the harmonic mean?

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