Data sufficiency for LIC AAO

Data sufficiency asks a different question from the rest of Quant. You are not asked for the answer. You are asked whether the information given is enough to find one answer. That changes how you work: you stop as soon as you know a unique value is possible, and you never need to finish the arithmetic. Candidates who solve every statement to the end lose time; candidates who assume information from one statement while testing the other lose marks.

The five options

A typical two-statement set uses these:

The method

1. Read the question and fix what is asked. "What is x?" needs one value. "What is A's share?" needs a number, not a ratio.
2. Test I alone. Cover statement II with your hand. Is a unique answer possible?
3. Test II alone. Now forget I completely. This is where most errors happen.
4. Only if neither works alone, test both together.
5. Stop as soon as you know. If an equation has one unknown and one linear equation, you know it can be solved. You do not need the value.

Why stop early: the marks are for the sufficiency judgement, not the number. Solving fully is useful only as a check when you are unsure.

Traps that decide the answer

• Squares give two values. x² = 64 gives x = 8 or −8. Unless something else rules out the negative, this is not sufficient.
• Two statements saying the same thing. "X is 25% more than Y" and "Y is 20% less than X" are the same fact. Together they are still one equation.
• Ratios without a total. A ratio of shares gives no rupee value until a total or one actual share is known.
• Hidden constraints. Lengths, speeds and counts of people are positive, and counts are whole numbers. Sometimes that removes the second value of a square.
• Carrying information across. When testing II alone, you may not use a fact from I.

Worked examples

Example 1. What is x?
I. 2x − 5 = 11
II. x² = 64
I gives x = 8, a unique value. II gives x = 8 or −8.
I alone.

Example 2. What is the annual premium P?
I. After a 10% increase it becomes ₹5,500.
II. It is ₹500 less than ₹5,500.
I: 1.1P = 5,500, so P = 5,000. II: P = 5,000.
Either alone.

Example 3. What is the area of a rectangle?
I. Its length is 12 cm.
II. Its perimeter is 40 cm.
Neither alone gives both sides. Together: 2(12 + b) = 40, so b = 8 and the area is 96.
Both together.

Example 4. What is A's share of a profit?
I. A and B invested in the ratio 3 : 2 for the same period.
II. The total profit is ₹50,000.
I gives a ratio but no amount. II gives an amount but no split. Together: 3/5 × 50,000 = 30,000.
Both together.

Example 5. What is P's age?
I. P is 4 years older than Q.
II. The ratio of P's age to Q's is 5 : 4.
Together: the ages are 5k and 4k, and 5k − 4k = 4 gives k = 4. P is 20.
Both together.

Example 6. What is the speed of a train?
I. It passes a pole in 12 seconds.
II. It passes a 200 m platform in 20 seconds.
Each alone has two unknowns, length L and speed v. Together: L = 12v and L + 200 = 20v, so 8v = 200 and v = 25 m/s.
Both together. This is a common case where each statement looks useless alone.

Example 7. What is the average age of five people?
I. The youngest is 20.
II. The oldest is 40.
The three middle ages are unknown even with both.
Not sufficient.

Example 8. How many policies did agent X sell?
I. X sold 25% more than Y.
II. Y sold 20% fewer than X.
If X = 1.25Y, then Y = 0.8X. Both statements say the same thing, and there is no actual number anywhere.
Not sufficient.

A quick check on common question types

Practice set

1. What is a car's speed? I. It covered 300 km. II. It took 5 hours. Both together. 300 ÷ 5 = 60 km/h.
2. What is A's age? I. A and B together are 50. II. A is 10 years older than B. Both together. A + B = 50 and A − B = 10 give A = 30.
3. What is x? I. x² − 5x + 6 = 0. II. x > 2.5. Both together. I gives 2 or 3; II alone gives no value; together x = 3.
4. What is the cost price of an article? I. It was sold for ₹1,200. II. The profit was 20%. Both together. CP = 1,200 ÷ 1.2 = 1,000.
5. What is the sum invested? I. The SI on it for 3 years at 8% is ₹2,400. II. The CI on it for 2 years at 10% is ₹2,100. Either alone. I: 2,400 ÷ 0.24 = 10,000. II: 2,100 ÷ 0.21 = 10,000.
6. How many days does A take alone? I. A and B together take 12 days. II. B alone takes 20 days. Both together. 1/12 − 1/20 = 1/30, so 30 days.
7. What is the average of four numbers? I. Their sum is 100. II. The largest is 40. I alone. 100 ÷ 4 = 25; II adds nothing.
8. What is the profit per cent? I. The CP of 10 articles is ₹500. II. The shopkeeper sold 8 articles. Not sufficient. No selling price is given anywhere.

What to do next

• For your next twenty DS questions, write "I alone: yes/no" and "II alone: yes/no" before looking at the options.
• Revise the arithmetic behind these in simple and compound interest and time, work and speed.
• Compare with the reasoning version in data sufficiency for reasoning, which uses the same options.