Quantitative data sufficiency for IBPS PO

A data sufficiency question asks something, then gives two or three statements. Your job is to decide whether the statements are enough to answer it. You do not need the answer itself, and working it out fully is usually a waste of time.

That makes DS a test of judgement more than calculation. The candidate who solves every equation to the end finishes late. The one who asks "does this pin down a single value?" and stops there finishes early. DS questions appear mostly in the mains, sometimes as a set of three to five, and they draw on every arithmetic topic: ages, interest, profit, speed, work and equations.

The standard options

The order and wording of options vary between papers. Read them once at the start of the set and note which letter means what. The examples in this guide use the letters above.

A checking order

1. Statement I alone. Does it give exactly one answer?
2. Statement II alone. Forget statement I completely while you test it.
3. Both together, only if neither works alone.
4. Stop as soon as you know. "One value" is sufficient; "two or more possible values" is not.

When is information enough?

Worked examples

Example 1: What is the value of x? I. x² = 49. II. x is positive.

• I alone: x = 7 or −7. Not sufficient.
• II alone: no value. Not sufficient.
• Together: x = 7. Answer: (d).

Example 2: What is x? I. 2x + 3y = 12. II. 4x + 6y = 24.

• Statement II is statement I multiplied by 2. Together they are still one equation in two unknowns.
• Answer: (e). This is the most common trap in DS.

Example 3: What is the profit percentage on an article? I. The cost price of 12 articles equals the selling price of 10. II. The selling price of one article is ₹60.

• I alone: let each article cost ₹1. Ten articles sell for ₹12 and cost ₹10, so profit = 2 ÷ 10 × 100 = 20%. Sufficient.
• II alone: no cost price. Not sufficient.
• Answer: (a). You did not need a single rupee value, because the question asks for a percentage.

Example 4: What is the area of a circle? I. Its circumference is 44 cm. II. Its diameter is 14 cm.

• I: 2πr = 44 gives r = 7 (with π = 22/7). Sufficient.
• II: r = 7. Sufficient.
• Answer: (c).

Example 5: What is P's present age? I. P is 4 years older than Q. II. Six years ago, the ratio of P's age to Q's age was 3 : 2.

• Each statement alone relates P to Q but gives no number.
• Together: P = Q + 4 and 2(P − 6) = 3(Q − 6). Substituting: 2Q − 4 = 3Q − 18, so Q = 14 and P = 18.
• Answer: (d). In the exam, stop at "two independent equations, two unknowns": that is enough.

Example 6: What is the speed of a boat in still water? I. It covers 24 km downstream in 2 hours. II. It covers 24 km upstream in 3 hours.

• I gives downstream speed 12 km/h only. II gives upstream speed 8 km/h only.
• Together: boat speed = (12 + 8) ÷ 2 = 10 km/h. Answer: (d).

Example 7 (yes/no): Is x greater than 5? I. x is greater than 7. II. x is less than 3.

• I: every such x is greater than 5. A definite yes. Sufficient.
• II: every such x is less than 5. A definite no. Sufficient.
• Answer: (c).

The trap: two possible answers

Example 8: What is the number? I. It is a two-digit prime. II. Its digits add up to 4.

• I alone: many primes. II alone: 13, 22, 31, 40.
• Together: 13 and 31 both fit. Two answers, so (e).

The three-statement version

Some papers give three statements and ask which combinations are sufficient. Test the pairs one by one.

Example 9: What is the simple interest earned? I. The principal is ₹8,000. II. The rate is 5% a year. III. The amount after 3 years is ₹9,200.

• I and II: no time. Not sufficient.
• I and III: SI = 9,200 − 8,000 = ₹1,200 for those 3 years. Sufficient.
• II and III: P × 1.15 = 9,200, so P = 8,000 and SI = ₹1,200. Sufficient.
• Answer: I and III together, or II and III together.

Common mistakes

• Letting statement I leak into statement II. Test II as if you had never read I.
• Solving to the end. Once you know a single value exists, stop.
• Missing a second root. x² = k has two roots unless something rules one out.
• Counting equations, not independent equations. Multiples of the same equation add nothing.
• Assuming what isn't stated. Unless the question says x is a positive integer, don't assume it.

Practice set

Use the options (a) to (e) as listed above.

1. What is the cost price of an item? I. It was sold for ₹600. II. The profit was 20%.
2. What is x? I. 2x + 3y = 12. II. x − y = 1.
3. How many days will A and B take together to finish a job? I. A alone takes 10 days. II. B alone takes 15 days.
4. What is the simple interest? I. The principal is ₹5,000 and the rate is 8% a year. II. The time is 3 years.
5. What is x? I. x² − 5x + 6 = 0. II. x > 2.
6. Is the integer x even? I. 3x is even. II. x + 5 is odd.
7. What is x? I. x + y = 10. II. 3x + 3y = 30.
8. What is the average of five numbers? I. The first three add up to 60 and the last two average 25. II. The largest number is 30.

Answers:

1. (d). Together, CP = 600 ÷ 1.2 = ₹500.
2. (d). Two independent equations: x = 3, y = 2.
3. (d). Together: 1/10 + 1/15 = 1/6, so 6 days.
4. (d). SI = 5,000 × 8 × 3 ÷ 100 = ₹1,200.
5. (d). I gives x = 2 or 3; II rules out 2, so x = 3.
6. (c). I: 3x even means x even. II: x + 5 odd means x even. Each alone gives a definite yes.
7. (e). II is I multiplied by 3.
8. (a). I: sum = 60 + 50 = 110, average 22. II alone says nothing about the sum.

What to do next

• Do ten DS questions a day for a week, writing only "S" or "NS" for each statement, never the full answer.
• Revise the arithmetic behind them: ratio and partnership and averages and ages supply many DS stems.
• Then practise quantity comparison, which rewards the same "enough or not" thinking.