LIC AAO quant revision sheet

This is the page to open ten minutes before a mock. It does not teach the topics from scratch. It lists the values and formulas that Quant questions in LIC AAO lean on, each with a quick example so you can check that you still remember how to use it. In a 20-minute prelims section with 35 questions, you have about 34 seconds a question. Anything you have to derive in the hall is time you do not have.

Fraction and percentage values

Check: 35 is what per cent of 280? 35/280 = 1/8 = 12.5%.

Squares and cubes

Simplification questions often hide these values. √576 = 24 and ∛1,728 = 12 should be recognition, not calculation.

Percentages

• Change = (new − old) ÷ old × 100. The base is always the old value.
• Successive changes of a% and b%: net = a + b + ab/100. Use negative signs for decreases.
• Successive discounts of a% and b%: net discount = a + b − ab/100.

Check: a price rises 20% and then falls 20%. Net = 20 − 20 + (20 × −20)/100 = −4%, a 4% fall.

Profit, loss and discount

• Profit and loss per cent are on the cost price. Discount per cent is on the marked price.
• SP = CP × (100 + profit%)/100.
• Two items sold at the same SP, one at x% profit and one at x% loss: always a loss of x²/100 per cent.

Check: marked price ₹800, discount 15%, cost ₹544. SP = 800 × 0.85 = ₹680. Profit = 136, and 136/544 = 25%.

Interest

• SI = P × R × T / 100.
• Amount under CI = P(1 + R/100)ⁿ.
• CI − SI for 2 years = P(R/100)².
• Half-yearly compounding: halve the rate, double the number of periods.

Check: on ₹10,000 at 10% for 2 years, CI − SI = 10,000 × (0.1)² = ₹100.

Ratio, average, partnership and mixtures

• When combining A : B and B : C, make the common term equal first.
• Total = average × count. A new member changes the average by (their value − old average) ÷ new count.
• Profit in a partnership is shared in the ratio of capital × time.
• Alligation: cheaper : dearer = (dearer price − mean price) : (mean price − cheaper price).

Check: A invests ₹40,000 for 12 months and B ₹60,000 for 6 months. Ratio = 4,80,000 : 3,60,000 = 4 : 3.

Time, work and speed

• Take the LCM of the days as total work. Each person's daily work = total ÷ their days. A pipe that empties counts as negative work.
• km/h × 5/18 = m/s. So 72 km/h = 20 m/s.
• Average speed over equal distances = 2ab/(a + b).
• Train passing a pole covers its own length; passing a platform covers train + platform.
• Boats: downstream = b + s, upstream = b − s. So b = (down + up)/2 and s = (down − up)/2.

Check: A takes 12 days, B 24 days. Work = 24 units; A does 2 a day, B 1. Together 3 a day, so 8 days.

Probability and counting

• P(not A) = 1 − P(A).
• nPr = n!/(n − r)!; nCr = n!/(r!(n − r)!).
• Two dice: 36 outcomes. Sum 7 comes 6 ways, so P = 1/6.
• One card from 52: 4 suits of 13, 12 face cards.

Check: choosing 2 of 5 people gives 5C2 = 10 ways.

Quadratic comparisons

Solve both equations, list all four roots, and compare every x with every y. If even one pair breaks a relation, choose "relation cannot be established".

Check: x² − 7x + 12 = 0 gives 3, 4. y² − 9y + 20 = 0 gives 4, 5. Pairs: 3 < 4, 3 < 5, 4 = 4, 4 < 5. So x ≤ y.

DI habits

• Read the title, units and headings before the questions.
• Compute shared totals once and write them down.
• Compare fractions by cross-multiplying.
• Percentage change uses the old value; share uses the total.
• Leave a slow set after two minutes and come back later.

Timing guide

Ten-question self-test

1. A value rises 20% then falls 20%. Net change?
2. CI − SI on ₹10,000 at 10% for 2 years?
3. Two items sell for ₹1,200 each, one at 20% profit and one at 20% loss. Overall?
4. Average speed for equal distances at 40 km/h and 60 km/h?
5. A takes 12 days, B 24 days. Together?
6. Probability of a sum of 7 with two dice?
7. 5C2?
8. 72 km/h in m/s?
9. Compare x and y: x² − 7x + 12 = 0, y² − 9y + 20 = 0.
10. Marked price ₹800, 15% discount, cost ₹544. Profit per cent?

Answers

1. 4% decrease. 20 − 20 − 400/100.
2. ₹100. 10,000 × 0.01.
3. 4% loss. 20²/100. In rupees: CPs are 1,000 and 1,500, total 2,500; SP total 2,400; loss 100 = 4%.
4. 48 km/h. 2 × 40 × 60 ÷ 100.
5. 8 days.
6. 1/6.
7. 10.
8. 20 m/s.
9. x ≤ y.
10. 25%.

What to do next

• Take this self-test cold. Any wrong answer marks a topic to revise today.
• Revise the full method for weak topics: profit and loss and simple and compound interest.
• For the mains, pair this sheet with the Data Analysis & Interpretation plan.