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Reasoning practice

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 do not have to find the final answer, only decide if it can be found. Bank exams ask them in the reasoning section, and some SSC papers include them. The main tip is to judge each statement alone first and only then combine them.

Rules to remember

  • A statement is sufficient only if it gives one definite answer to the question.
  • For a yes or no question, a definite 'no' is also sufficient. Only a 'sometimes yes, sometimes no' result is not sufficient.
  • Option set used in this guide: (A) I alone is sufficient; (B) II alone is sufficient; (C) both together are needed; (D) each alone is sufficient; (E) both together are still not sufficient. Always read the option wording in your paper, as the order can change.
  • Step 1: read statement I alone and ignore II. Step 2: read statement II alone and ignore I. Step 3: only then combine them.
  • To find n unknown values you generally need n separate equations. Two statements that say the same thing count as one.
  • Do not use outside facts, except common knowledge such as 1 hour = 60 minutes.
  • Watch for equations like x squared = 9. They give two values (3 and -3) unless another clue removes one.
  • For ranking questions, rank from top + rank from bottom = total + 1.

Worked examples

Q1. What is the speed of a car? I. The car covers 150 km in 3 hours. II. The car is red. Options: (A) I alone (B) II alone (C) both together (D) each alone (E) both together are not sufficient

  1. Statement I alone: speed = distance / time = 150 / 3 = 50 km/h. This is a definite answer.
  2. Statement II alone: the colour of the car has nothing to do with its speed. It is not sufficient.
  3. Only statement I is sufficient.

Answer: (A) Statement I alone

Q2. What is the value of x? I. x squared = 9. II. x > 0. Options: (A) I alone (B) II alone (C) both together (D) each alone (E) both together are not sufficient

  1. Statement I alone: x squared = 9 gives x = 3 or x = -3. Two values, so it is not sufficient.
  2. Statement II alone: x > 0 allows any positive number. Not sufficient.
  3. Together: x is 3 or -3, and x must be positive, so x = 3. One definite value.
  4. Both statements are needed.

Answer: (C) Both together

Q3. In a class of 30 students, what is Dev's rank from the top? I. Dev's rank from the bottom is 12. II. There are 18 students above Dev. Options: (A) I alone (B) II alone (C) both together (D) each alone (E) both together are not sufficient

  1. Statement I alone: rank from top = 30 + 1 - 12 = 19. Definite answer, so I is sufficient.
  2. Statement II alone: if 18 students are above Dev, Dev's rank from the top is 18 + 1 = 19. Definite answer, so II is sufficient.
  3. Each statement alone gives the same rank. They also agree with each other: 18 above, Dev, and 11 below make 30.

Answer: (D) Each alone is sufficient

Shortcuts that save time

  • Never merge the statements before you have tested each alone. Students who combine too early often mark 'both together' when one statement was enough, and lose marks.
  • Decide sufficiency, not the value. The moment you know a statement gives exactly one answer, stop calculating and move on. This saves time for longer questions.
  • Eliminate options in pairs. If statement I alone fails and statement II alone fails, only the 'both together' and 'neither' options remain. This cuts the risk of a random guess.

Where this appears

IBPS PO PrelimsReasoning Ability section
IBPS PO MainsReasoning & Computer Aptitude section
SBI PO PrelimsReasoning Ability section
SSC CGL Tier-1General Intelligence & Reasoning section

Data Sufficiency

Practice Set
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What is the value of a certain two-digit number? I. The units digit of the number is 9. II. The product of the digits of the number is 36.

Reasoning · stress-free practice · answers reveal instantly

Data Sufficiency questions with answers

10 sample questions from this topic with the correct option and the solution.

  1. Q1. What is the value of a certain two-digit number? I. The product of the digits of the number is 0. II. The sum of the digits of the number is 8.

    1. Either statement I or II alone is sufficient
    2. Both statements I and II together are needed, but neither alone is sufficient
    3. Statement II alone is sufficient, but Statement I alone is not sufficient
    4. Statement I alone is sufficient, but Statement II alone is not sufficient

    Answer: (B) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 9 possible number(s); Statement II alone gives 8 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  2. Q2. What is the value of a certain two-digit number? I. The tens digit of the number is 3. II. The product of the digits of the number is 24.

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

    Answer: (A) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 10 possible number(s); Statement II alone gives 4 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  3. Q3. What is the value of a certain two-digit number? I. The product of the digits of the number is 35. II. The sum of the digits of the number is 12.

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

    Answer: (C) Even both statements I and II together are not sufficient

    Solution
    Statement I alone gives 2 possible number(s); Statement II alone gives 7 possible number(s); together they give 2 possible number(s). Hence, 'Even both statements I and II together are not sufficient'.

  4. Q4. What is the value of a certain two-digit number? I. The number lies between 40 and 48 (both exclusive). II. The sum of the digits of the number is 8.

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

    Answer: (D) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 7 possible number(s); Statement II alone gives 8 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  5. Q5. What is the value of a certain two-digit number? I. The number lies between 76 and 83 (both exclusive). II. The units digit of the number is 9.

    1. Both statements I and II together are needed, but neither alone is sufficient
    2. Statement I alone is sufficient, but Statement II alone is not sufficient
    3. Statement II alone is sufficient, but Statement I alone is not sufficient
    4. Even both statements I and II together are not sufficient

    Answer: (A) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 6 possible number(s); Statement II alone gives 9 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  6. Q6. What is the value of a certain two-digit number? I. The tens digit of the number is 3. II. The number is divisible by 9.

    1. Both statements I and II together are needed, but neither alone is sufficient
    2. Statement I alone is sufficient, but Statement II alone is not sufficient
    3. Even both statements I and II together are not sufficient
    4. Statement II alone is sufficient, but Statement I alone is not sufficient

    Answer: (A) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 10 possible number(s); Statement II alone gives 10 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  7. Q7. What is the value of a certain two-digit number? I. The tens digit of the number is 6. II. The number is divisible by 8.

    1. Both statements I and II together are needed, but neither alone is sufficient
    2. Statement I alone is sufficient, but Statement II alone is not sufficient
    3. Statement II alone is sufficient, but Statement I alone is not sufficient
    4. Even both statements I and II together are not sufficient

    Answer: (A) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 10 possible number(s); Statement II alone gives 11 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  8. Q8. What is the value of a certain two-digit number? I. The number lies between 24 and 32 (both exclusive). II. The units digit of the number is 9.

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

    Answer: (D) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 7 possible number(s); Statement II alone gives 9 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  9. Q9. What is the value of a certain two-digit number? I. The tens digit of the number is 3. II. The units digit of the number is 5.

    1. Statement II alone is sufficient, but Statement I alone is not sufficient
    2. Either statement I or II alone is sufficient
    3. Both statements I and II together are needed, but neither alone is sufficient
    4. Statement I alone is sufficient, but Statement II alone is not sufficient

    Answer: (C) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 10 possible number(s); Statement II alone gives 9 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.

  10. Q10. What is the value of a certain two-digit number? I. The units digit of the number is 8. II. The sum of the digits of the number is 13.

    1. Statement I alone is sufficient, but Statement II alone is not sufficient
    2. Either statement I or II alone is sufficient
    3. Statement II alone is sufficient, but Statement I alone is not sufficient
    4. Both statements I and II together are needed, but neither alone is sufficient

    Answer: (D) Both statements I and II together are needed, but neither alone is sufficient

    Solution
    Statement I alone gives 9 possible number(s); Statement II alone gives 6 possible number(s); together they give 1 possible number(s). Hence, 'Both statements I and II together are needed, but neither alone is sufficient'.