Quantitative data sufficiency for SBI PO

Data sufficiency (DS) asks whether the information given is enough to answer a question. It does not ask for the answer. That single difference makes DS the fastest quant type for a disciplined candidate and one of the slowest for an undisciplined one, who solves every statement to the last digit and then picks an option.

DS sets appear in the SBI PO mains quant section alongside DI, and the same logic drives the reasoning version of DS. This guide gives the standard options, a method that avoids the usual traps, and worked examples from the arithmetic topics that DS draws on.

The usual options

1. Statement I alone is sufficient, but II alone is not.
2. Statement II alone is sufficient, but I alone is not.
3. Either statement alone is sufficient.
4. Both statements together are needed; neither alone is enough.
5. Even both together are not sufficient.

The wording and order vary between papers, so read the options once at the start of a set. Some bank PO papers also use three statements, with options such as "only I and III together". The method below works the same way.

The method

1. Test I alone. Can it produce exactly one answer? Don't finish the arithmetic; just check that it could be finished.
2. Test II alone, and forget everything statement I told you.
3. Only if neither works alone, combine them.
4. Stop the moment you know whether a single answer exists.

Why "exactly one answer" is the test. A statement is sufficient only if it pins the answer down. If it allows two values (x = 5 or −5), it is not sufficient, even if one value looks more natural.

Yes/no questions. For "Is x > 10?", a statement is sufficient if it gives a definite yes or a definite no. A definite no is still sufficient. It is only insufficient when the answer could be either.

Worked examples

Example 1. What is the value of x?
I. 3x + 2 = 17
II. x² = 25

• I: x = 5, one value. Sufficient.
• II: x = 5 or −5. Not sufficient.
• I alone is sufficient.

Example 2. What is the principal?
I. Simple interest for 2 years at 10% a year is ₹2,000.
II. Compound interest for 2 years at 10% a year, compounded annually, is ₹2,100.

• I: P × 10 × 2 ÷ 100 = 2,000, so P = 10,000.
• II: P × (1.21 − 1) = 2,100, so P = 10,000.
• Either statement alone is sufficient.

Example 3. Is x > 10?
I. 2x − 5 > 17
II. x² > 100

• I: 2x > 22, so x > 11. Definitely yes. Sufficient.
• II: x > 10 or x < −10. Could be yes or no. Not sufficient.
• I alone is sufficient.

Example 4. A definite no. Is y a prime number?
I. y = 4k, where k is a positive integer.
II. y is a two-digit number.

• I: y is a multiple of 4, so it has 2 as a factor and is at least 4. It can never be prime. A definite no, so sufficient.
• II: y could be 11 (prime) or 12 (not prime). Not sufficient.
• I alone is sufficient. Many candidates mark "not sufficient" for I because the answer is "no". That is the trap.

Example 5. What is the present age of Q?
I. The ratio of P's age to Q's age now is 4 : 5.
II. Six years ago, the ratio of their ages was 3 : 4.

• Each alone is a ratio with no size, so neither is enough.
• Together: (4k − 6) : (5k − 6) = 3 : 4 gives 16k − 24 = 15k − 18, so k = 6. You can stop here; Q = 30.
• Both together are needed.

Example 6. What is the profit percentage on an article?
I. The marked price is 25% above the cost price.
II. A discount of 20% is given on the marked price.

• Neither alone links cost and selling price.
• Together: CP 100, MP 125, SP 125 × 0.8 = 100. The profit is 0%.
• Both together are needed. A 0% answer is still a unique answer.

Example 7. In how many days can A alone finish a job?
I. A and B together finish it in 8 days.
II. B and C together finish it in 12 days.

• Together you have two equations and three unknowns (A, B and C's rates).
• Even both together are not sufficient.

Example 8. What is the speed of the boat in still water?
I. The boat covers 24 km downstream in 2 hours.
II. The boat covers the same 24 km upstream in 3 hours.

• I gives the downstream speed, 12 km/h, but not the stream's speed.
• II gives the upstream speed, 8 km/h, alone.
• Together: boat speed = (12 + 8) ÷ 2 = 10 km/h.
• Both together are needed.

Traps

Practice set

1. What is the area of a rectangle? I. Its perimeter is 30 cm. II. Its length is 10 cm.
2. In how many days can A alone finish a job? I. A and B together take 6 days. II. B alone takes 10 days.
3. What is the cost price of an article? I. It was sold at a 20% profit. II. It was sold for ₹600.
4. n is an integer. Is n even? I. n² is even. II. 3n is even.
5. What is the rate of simple interest a year? I. A sum doubles in 8 years. II. The simple interest on ₹5,000 for 3 years is ₹1,875.
6. What is the speed of the stream? I. The boat's upstream speed is 8 km/h. II. The boat's speed in still water is 10 km/h.

Answers:

1. Both together. Breadth = 15 − 10 = 5 cm, so area = 50 cm². Neither alone is enough.
2. Both together. A's rate = 1/6 − 1/10 = 1/15, so 15 days.
3. Both together. CP = 600 ÷ 1.2 = ₹500.
4. Either alone. If n² is even, n is even, because an odd number squared is odd. If 3n is even, n is even, because 3 is odd.
5. Either alone. I: interest equals principal in 8 years, so R = 100 ÷ 8 = 12.5%. II: 1,875 = 5,000 × R × 3 ÷ 100, so R = 12.5%.
6. Both together. Stream speed = 10 − 8 = 2 km/h.

What to do next

• For your next 20 DS questions, write only "suff" or "not suff" next to each statement. Don't calculate final answers.
• Revise the topics DS draws on: profit and loss and simple and compound interest.
• Compare this with the reasoning version of data sufficiency, which uses the same options.
• Next, practise quantity comparison, the other logic-heavy quant type.