Data Sufficiency Questions with Answers
Data sufficiency questions give you a question and two statements, and ask whether the statements contain enough information to answer it. You don’t need to solve for the final value. Test statement 1 alone, then statement 2 alone, then both together, and pick the option that says which of them is enough.
Data sufficiency is a reasoning question type, and our Accenture guide lists it among the topics prep sites report for critical reasoning. It sits alongside syllogisms and coding-decoding as a question type where the skill is judging information, not computing.
What Are Data Sufficiency Questions?
Each question has a main question and two statements, usually labelled I and II (or 1 and 2). The statements may be numbers, facts about people, or conditions. Your job is to decide whether they give enough information to answer the main question with one definite answer.
A statement is sufficient when it leads to exactly one answer. For a yes/no question, a definite “no” is as sufficient as a definite “yes”. A statement is not sufficient when it leaves two or more possible answers, or doesn’t touch the question at all.
The Five Answer Options
Most papers use the same five options, though the exact wording and order change from paper to paper. Read the options given in your test.
| Option | Meaning |
|---|---|
| 1 | Statement I alone is sufficient, and statement II alone is not |
| 2 | Statement II alone is sufficient, and statement I alone is not |
| 3 | Both statements together are sufficient, but neither alone is |
| 4 | Either statement alone is sufficient |
| 5 | Neither statement is sufficient, even together |
Some papers give only four options, and some merge options 4 and 5 differently. Always check the labels before you answer.
A Step-by-Step Method
- Read the main question first and be clear about what you must find. Is it a value, or a yes/no?
- Look at statement I alone. Ignore statement II completely. Does it give one definite answer?
- Look at statement II alone. Ignore statement I completely.
- If neither works alone, combine them. Do the two together give one definite answer?
- Choose the option that matches what you found. If both work alone, it is “either”. If neither works even together, it is “neither”.
- Don’t solve fully. Stop as soon as you know whether the answer can be found. Computing the exact value wastes time.
Solved Examples
1. A statement that gives two values. What is the value of x? (I) 3x - 5 = 10. (II) x^2 = 25. Answer: statement I alone. From I, 3x = 15, so x = 5. From II, x could be 5 or -5, which is two values, so II is not sufficient.
2. A yes/no question. Is the integer n even? (I) n + 1 is odd. (II) n is a multiple of 3. Answer: statement I alone. If n + 1 is odd, n must be even, so I gives a definite “yes”. Multiples of 3 include 3 (odd) and 6 (even), so II doesn’t decide it.
3. Both statements needed. What is Ravi’s age? (I) Ravi is 4 years older than Sita. (II) Sita is 20 years old. Answer: both together. I alone gives only a difference, and II alone says nothing about Ravi. Together, Ravi is 20 + 4 = 24.
4. Either statement works. What is the area of a square? (I) Its perimeter is 20 cm. (II) Its diagonal is 5 x sqrt(2) cm. Answer: either statement alone. From I, the side is 20 / 4 = 5 cm. From II, the side is the diagonal divided by sqrt(2), which is also 5 cm. Either way, the area is 25 square cm.
5. Neither is enough. What is the value of y? (I) y > 3. (II) y < 10. Answer: neither, even together. Together they say y is between 3 and 10, which allows many values.
6. A trap with a squared term. Is x greater than 0? (I) x^2 > 0. (II) x^3 > 0. Answer: statement II alone. x^2 > 0 only says x isn’t zero, so x could be -2 or 2, and I is not sufficient. A cube keeps the sign of x, so x^3 > 0 means x > 0, which is a definite “yes”.
7. Extra information that doesn’t help. A car travels 120 km. What is its average speed? (I) The trip took 2 hours. (II) The car covered 60 km in the first hour. Answer: statement I alone. Average speed is total distance divided by total time, so 120 / 2 = 60 km/h. Statement II only describes the first hour, so it doesn’t give the whole trip’s time.
Common Mistakes
- Using both statements at once. Test each statement alone first. Mixing them early hides the cases where one alone is enough.
- Treating two possible values as sufficient. If a statement allows two answers, as x^2 = 25 does, it is not sufficient.
- Assuming a “no” is insufficient. In a yes/no question, a definite “no” counts as an answer.
- Using outside facts. Don’t assume numbers or conditions that aren’t given. Everyday facts that are always true, such as 60 minutes in an hour, are fine.
- Solving the whole problem. You only need to know whether an answer exists, not what it is.
- Skipping the option wording. The option order and labels can differ from the table above.
Practice Questions
Try each on paper, then check the answer. Options are written in words, so match them to your paper’s labels.
1. What is the price of one pen? (I) 4 pens cost Rs 48. (II) A pen costs Rs 2 more than a pencil. Answer: statement I alone. 48 / 4 = Rs 12 per pen. Statement II compares with a pencil whose price is unknown.
2. How many students are in a class? (I) 40% of the students are girls. (II) There are 18 boys. Answer: both together. Boys are 60% of the class, so 18 is 60% of the total, which gives 30. Neither statement works alone.
3. Is x an even number? (I) x is divisible by 3. (II) x is divisible by 4. Answer: statement II alone. Every multiple of 4 is even. Multiples of 3 include 3 (odd) and 6 (even), so I doesn’t decide it.
4. What is the value of a? (I) a^2 = 9. (II) a > 0. Answer: both together. I allows 3 or -3, and II alone allows any positive number. Together, a = 3.
5. What is the area of a rectangle? (I) Its length is 10 cm. (II) Its diagonal is longer than 10 cm. Answer: neither, even together. The width is never fixed, so the area can’t be found.
6. Is p greater than q? (I) p = 2q. (II) q > 0. Answer: both together. From I alone, if q = -1 then p = -2, which is less than q. If q = 1 then p = 2, which is greater. II alone says nothing about p. Together, q is positive, so p = 2q is greater than q.
7. What is the cost of 1 kg of rice? (I) 5 kg cost Rs 250. (II) 10 kg cost Rs 500. Answer: either statement alone. I gives 250 / 5 = Rs 50 per kg, and II gives 500 / 10 = Rs 50 per kg.
8. Is y a prime number? (I) y is an even number. (II) y > 2. Answer: both together. An even number could be 2 (prime) or 4 (not prime), and y > 2 alone allows both primes and non-primes. Together, y is even and greater than 2, so it is divisible by 2 and isn’t prime. That is a definite “no”.
Frequently Asked Questions
What are data sufficiency questions?
They give a question and two statements, and ask whether the statements provide enough information to answer it. You judge sufficiency instead of working out the final answer.
How do I solve data sufficiency questions?
Read the question, test statement I alone, test statement II alone, and combine them only if neither works alone. Then pick the option that matches. Stop as soon as you know whether an answer can be found.
What does “sufficient” mean in data sufficiency?
A statement is sufficient when it leads to one definite answer. For a yes/no question, a definite “no” counts. If it allows two or more answers, it is not sufficient.
What are the answer options in data sufficiency?
The usual five are: I alone, II alone, both together, either alone, and neither even together. The wording and order change between papers, so read the options on your own test.
Do I need to calculate the exact answer?
Usually not. You only need to know whether the answer can be found. Calculating the exact value takes time you don’t need to spend.
Which exams ask data sufficiency questions?
They appear in the reasoning sections of many bank and SSC exams. Prep sites also report them among critical reasoning topics for Accenture, as covered in our Accenture guide.