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Data Sufficiency in Quant: Decide Without Solving Fully

The five options • Test I, then II, then both • Sufficient means one value • Stop before the arithmetic

Banking 📅 Last updated: 2026-10-24

A data sufficiency question gives a question and two statements, I and II. You do not have to answer the question. You have to decide whether the statements give enough information to answer it, and which statements are needed. Bank exams usually offer five standard 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 sufficient.
  5. Both statements together are still not sufficient.

"Sufficient" means the data fixes one answer. If a statement allows two or more answers, it is not sufficient, even if you could list them all.

  1. Test statement I alone. Ignore II completely.
  2. Test statement II alone. Now ignore I completely.
  3. Only if both fail alone, combine them and test again.

Work only as far as needed to know whether one value is fixed. Setting up one equation in one unknown is enough to show sufficiency; you do not need to solve it.

Worked example 1: one statement works, one does not

What is x? I. 3x + 5 = 20. II. x² = 25. From I, x = (20 − 5) ÷ 3 = 5, one value. From II, x could be 5 or −5, two values. Answer: I alone is sufficient.

Notice that both statements are consistent with x = 5, but that does not make II sufficient. Sufficiency is about whether a statement fixes the answer by itself.

Many questions have two unknowns, and each statement supplies one equation. Then neither alone works, but together they do.

Worked example 2: train speed

What is the speed of a train? I. It crosses a 200 m platform in 20 seconds. II. It crosses a pole in 12 seconds. Each statement involves the unknown length L as well as the speed. Together: L + 200 = 20v and L = 12v, so 8v = 200 and v = 25 m/s = 90 km/h. Answer: both together are needed.

Worked example 3: ages from a ratio and a sum

What is A's age? I. A's and B's ages are in the ratio 3 : 4. II. The sum of their ages is 42. A ratio alone has no scale, and a sum alone has no split. Together, A = 42 × 3/7 = 18. Answer: both together.

Sometimes each statement on its own fixes the answer. That is the "either" option, and it is easy to miss if you stop after finding statement I sufficient.

Worked example 4: either statement alone

What is the principal? I. The simple interest for 2 years at 10% a year is ₹2,000. II. The amount after 2 years at 10% simple interest is ₹12,000. From I, P = 2,000 × 100 ÷ (10 × 2) = ₹10,000.

From II alone, P = 12,000 ÷ (1 + 10 × 2/100) = ₹10,000 as well. Each statement is sufficient on its own, so the answer is either alone.

Worked example 5: neither, even together

What is the profit percentage on an article? I. Its cost price is ₹400. II. Its marked price is ₹600. Profit depends on the selling price, and neither statement says what discount, if any, was given. Even together, the selling price is unknown. Answer: both together are not sufficient.

  • ✘ Carrying information from statement I into the test of statement II alone.
  • ✘ Treating a statement that allows two answers, such as x² = 25, as sufficient.
  • ✘ Stopping once I is sufficient and missing that II is also sufficient (the "either" case).
  • ✘ Solving to the final number when only sufficiency is asked.
  • ✘ Assuming unstated facts, for example that a number is positive or an integer, unless the question says so.
I aloneII aloneTogetherAnswer
SufficientNot—I alone
NotSufficient—II alone
SufficientSufficient—Either alone
NotNotSufficientBoth needed
NotNotNotNot sufficient

Most data sufficiency questions reuse standard topics: trains, ages, simple interest and time and work. The other bank prelims sets are number series, approximation and quantity comparison; formulas are in the Quant cheat code.

Q1. What is the area of a rectangle? I. Its length is 12 cm and its perimeter is 40 cm. II. Its diagonal is 15 cm. easy

✅ Answer: (a) I alone is sufficient

💡 Explanation: From I, breadth = 40 ÷ 2 − 12 = 8 cm, so the area is 96 cm². A diagonal alone fits many rectangles, so II is not sufficient.

Q2. What is the value of the positive number n? I. n is a two-digit prime number. II. n² = 169. easy

✅ Answer: (c) II alone is sufficient

💡 Explanation: Statement I fits 11, 13, 17 and many more primes, so it is not enough. Statement II with n positive gives exactly n = 13, so II alone is sufficient.

Q3. In how many days can A and B together finish a job? I. A alone takes 12 days. II. B alone takes 18 days. easy

✅ Answer: (d) Both together are needed

💡 Explanation: Each statement gives only one worker's time. Together they give the combined time 12 × 18 ÷ 30 = 7.2 days, so both statements are needed.

Q4. How many students are in a class? I. The class's total marks are 1,800 and its average is 60. II. If 5 more students join, the class will have 35 students. medium

✅ Answer: (b) Either I or II alone is sufficient

💡 Explanation: Statement I gives 1,800 ÷ 60 = 30 students. Statement II gives 35 − 5 = 30 students. Each alone gives the same single answer, so either is sufficient.

Q5. What is the speed of a boat in still water? I. Its downstream speed is 15 km/h. II. The stream is slower than the boat. medium

✅ Answer: (d) Neither is sufficient, even together

💡 Explanation: Still-water speed needs both the downstream and upstream speeds, or one of them with the stream speed. II only says the stream is slower, which gives no number, so even together the statements are not enough.

Q6. What is the annual rate of compound interest? I. The principal is ₹8,000. II. The amount after 2 years, compounded annually, is ₹9,680. medium

✅ Answer: (a) Both together are needed

💡 Explanation: Neither statement alone fixes the rate. Together, (1 + r)² = 9,680 ÷ 8,000 = 1.21, so 1 + r = 1.1 and the rate is 10%. Both are needed.

Do I need to calculate the final answer in data sufficiency?

No. You only need to know whether a single answer can be found. Once you see that the statements fix one value, stop and mark the option; the actual number is never asked. Calculating fully wastes the time that makes data sufficiency quick.

What is the most common mistake in data sufficiency?

Using information from one statement while judging the other alone. When you test statement II by itself, forget everything statement I said. Only when both fail alone should you combine them and test again.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 10 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-24 against the sources listed above.

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