InterviewSam
Log inStart free

Data Sufficiency

Decide which statements are enough to answer.

45 solved questions · 15 easy · 20 medium · 10 hard

Take a 10-question quiz on Data Sufficiency, no login

Shortcuts & formulas

  • Test each statement alone first, then both together; only combine if neither is enough by itself.
  • A statement is sufficient only if it gives ONE definite answer. For a Yes/No question, a definite 'No' is also sufficient.
  • Two unknowns need two independent equations: sum alone or difference alone is not enough, but sum + difference together is.
  • A ratio gives the shape but not the size: you need one actual value (a total, a difference or one quantity) as well.
  • Never use outside guesses: if a value can change while the statement stays true, the statement is not sufficient.
  • Ordering questions: draw the chain from each statement; if the asked position still has two candidates, the data is not sufficient.
  • Standard options: I alone / II alone / either alone / both together needed / even both together not enough.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is the sum of the ages of Kiran and Asha? Statement I: The sum of their ages is 70 years. Statement II: Kiran is 39 years old.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the sum of their ages = 70 in every possible case, so I alone is sufficient. From II: the sum of their ages can be 40, 41, 42, 43, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q2.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x? Statement I: y = 13. Statement II: x = 24.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: x can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: x = 24 in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q3.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many boys are there in the class? Statement I: There are 6 fewer boys than girls. Statement II: The class has 17 girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the number of boys can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: the number of boys can be 1, 2, 3, 4, ..., so II alone is not sufficient. I and II together: only 11 is possible for the number of boys, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q4.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is the sum of the ages of Meena and Asha? Statement I: Meena is older than Asha. Statement II: Meena is 42 years old.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: the sum of their ages can be 3, 4, 5, 6, ..., so I alone is not sufficient. From II: the sum of their ages can be 43, 44, 45, 46, ..., so II alone is not sufficient. Even together, the sum of their ages can still be 43, 44, 45, 46, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q5.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x + y? Statement I: x - y = -13. Statement II: y = 21.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: x + y can be 15, 17, 19, 21, ..., so I alone is not sufficient. From II: x + y can be 22, 23, 24, 25, ..., so II alone is not sufficient. I and II together: only 29 is possible for x + y, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q6.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many students are there in the class? Statement I: The total number of students is 45. Statement II: The class has 22 boys.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the number of students = 45 in every possible case, so I alone is sufficient. From II: the number of students can be 23, 24, 25, 26, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q7.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is the sum of the ages of Suresh and Kiran? Statement I: Suresh is 37 years old. Statement II: Suresh is older than Kiran.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: the sum of their ages can be 38, 39, 40, 41, ..., so I alone is not sufficient. From II: the sum of their ages can be 3, 4, 5, 6, ..., so II alone is not sufficient. Even together, the sum of their ages can still be 38, 39, 40, 41, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q8.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x + y? Statement I: y = 9. Statement II: x + y = 33.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: x + y can be 10, 11, 12, 13, ..., so I alone is not sufficient. From II: x + y = 33 in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q9.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many girls are there in the class? Statement I: There are 21 fewer boys than girls. Statement II: The class has 13 boys.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the number of girls can be 22, 23, 24, 25, ..., so I alone is not sufficient. From II: the number of girls can be 1, 2, 3, 4, ..., so II alone is not sufficient. I and II together: only 34 is possible for the number of girls, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q10.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is the sum of the ages of Meena and Divya? Statement I: The sum of their ages is 64 years. Statement II: Meena is older than Divya.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the sum of their ages = 64 in every possible case, so I alone is sufficient. From II: the sum of their ages can be 3, 4, 5, 6, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q11.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x? Statement I: x + y = 40. Statement II: x = 26.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: x can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: x = 26 in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q12.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many students are there in the class? Statement I: There are 12 fewer boys than girls. Statement II: The class has 14 boys.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the number of students can be 14, 16, 18, 20, ..., so I alone is not sufficient. From II: the number of students can be 15, 16, 17, 18, ..., so II alone is not sufficient. I and II together: only 40 is possible for the number of students, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q13.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is Suresh's age? Statement I: Suresh is older than Asha. Statement II: Suresh is 10 years older than Asha.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: Suresh's age can be 2, 3, 4, 5, ..., so I alone is not sufficient. From II: Suresh's age can be 11, 12, 13, 14, ..., so II alone is not sufficient. Even together, Suresh's age can still be 11, 12, 13, 14, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q14.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x + y? Statement I: x = 18. Statement II: x - y = -6.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: x + y can be 19, 20, 21, 22, ..., so I alone is not sufficient. From II: x + y can be 8, 10, 12, 14, ..., so II alone is not sufficient. I and II together: only 42 is possible for x + y, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q15.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many boys are there in the class? Statement I: The class has 26 boys. Statement II: Boys are fewer in number than girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the number of boys = 26 in every possible case, so I alone is sufficient. From II: the number of boys can be 1, 2, 3, 4, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Medium questions

Q16.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is the sum of the ages of Arjun and Divya? Statement I: Arjun is older than Divya. Statement II: The ages of Arjun and Divya are in the ratio 4:1.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: the sum of their ages can be 3, 4, 5, 6, ..., so I alone is not sufficient. From II: the sum of their ages can be 5, 10, 15, 20, ..., so II alone is not sufficient. Even together, the sum of their ages can still be 5, 10, 15, 20, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q17.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of x? Statement I: x - y = -12. Statement II: x - y = -12 and y = 23.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: x can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: x = 11 in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q18.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: Are there more than 14 girls in the class? Statement I: The total number of students is 23. Statement II: There are 1 fewer boys than girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the answer can be Yes (for example boys = 1, girls = 22) or No (for example boys = 9, girls = 14), so I alone is not sufficient. From II: the answer can be Yes (for example boys = 14, girls = 15) or No (for example boys = 1, girls = 2), so II alone is not sufficient. I and II together: the answer is always No, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q19.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the length of the rectangle? Statement I: The perimeter is 78 cm and the length is 30 cm. Statement II: The length exceeds the breadth by 21 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the length = 30 in every possible case, so I alone is sufficient. From II: the length can be 22, 23, 24, 25, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q20.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Divya, Suresh, Ravi, Kiran. Question: Who is the shortest of the four? Statement I: Divya is taller than Kiran. Statement II: Kiran is the shortest.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: the shortest person can be Kiran, Ravi, Suresh, so I alone is not sufficient. From II: the shortest person = Kiran in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q21.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: Is Kiran older than Rohit? Statement I: Rohit is 5 years old. Statement II: The sum of their ages is 60 years.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the answer can be Yes (for example Kiran = 6, Rohit = 5) or No (for example Kiran = 1, Rohit = 5), so I alone is not sufficient. From II: the answer can be Yes (for example Kiran = 31, Rohit = 29) or No (for example Kiran = 1, Rohit = 59), so II alone is not sufficient. I and II together: the answer is always Yes, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q22.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of y? Statement I: x + y = 43. Statement II: x is greater than y.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: y can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: y can be 1, 2, 3, 4, ..., so II alone is not sufficient. Even together, y can still be 1, 2, 3, 4, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q23.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: Are there more boys than girls in the class? Statement I: There are 21 fewer boys than girls. Statement II: Boys are fewer in number than girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: C. Either statement alone is sufficient

Solution

From I: the answer = No in every possible case, so I alone is sufficient. From II: the answer = No in every possible case, so II alone is sufficient. Answer: Either statement alone is sufficient

Q24.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the area of the rectangle? Statement I: The length is 2 times the breadth. Statement II: The perimeter is 60 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the area can be 2, 8, 18, 32, ..., so I alone is not sufficient. From II: the area can be 29, 56, 81, 104, ..., so II alone is not sufficient. I and II together: only 200 is possible for the area, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q25.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Meena, Divya, Kiran, Ravi. Question: Who is the tallest of the four? Statement I: Meena is the tallest. Statement II: Divya is taller than Kiran.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the tallest person = Meena in every possible case, so I alone is sufficient. From II: the tallest person can be Divya, Meena, Ravi, so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q26.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is Kiran's age? Statement I: Kiran's age is a multiple of 4. Statement II: Divya is 40 years old.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: Kiran's age can be 4, 8, 12, 16, ..., so I alone is not sufficient. From II: Kiran's age can be 1, 2, 3, 4, ..., so II alone is not sufficient. Even together, Kiran's age can still be 4, 8, 12, 16, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q27.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: Is x greater than y? Statement I: xy = 325. Statement II: x - y = 12 and y = 13.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: the answer can be Yes (for example x = 25, y = 13) or No (for example x = 13, y = 25), so I alone is not sufficient. From II: the answer = Yes in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q28.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: How many students are there in the class? Statement I: The class has 45 boys. Statement II: The class has 27 girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the number of students can be 46, 47, 48, 49, ..., so I alone is not sufficient. From II: the number of students can be 28, 29, 30, 31, ..., so II alone is not sufficient. I and II together: only 72 is possible for the number of students, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q29.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the area of the rectangle? Statement I: The area is 57 sq cm. Statement II: The breadth is 3 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the area = 57 in every possible case, so I alone is sufficient. From II: the area can be 3, 6, 9, 12, ..., so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q30.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Suresh, Ravi, Divya, Kiran. Question: Is Kiran taller than Ravi? Statement I: Divya is not the shortest. Statement II: Kiran is shorter than both Suresh and Ravi.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: the answer can be Yes (for example order (tallest first): Suresh, Divya, Kiran, Ravi) or No (for example order (tallest first): Suresh, Ravi, Divya, Kiran), so I alone is not sufficient. From II: the answer = No in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q31.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: What is Asha's age? Statement I: Kiran is 3 years younger than Asha. Statement II: The sum of their ages is 49 years.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: Asha's age can be 4, 5, 6, 7, ..., so I alone is not sufficient. From II: Asha's age can be 1, 2, 3, 4, ..., so II alone is not sufficient. I and II together: only 26 is possible for Asha's age, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q32.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: What is the value of y? Statement I: x + y = 36. Statement II: x is less than y.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: y can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: y can be 2, 3, 4, 5, ..., so II alone is not sufficient. Even together, y can still be 19, 20, 21, 22, ..., so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q33.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: Are there more boys than girls in the class? Statement I: The total is 48 and there are 25 boys. Statement II: There are 2 more boys than girls.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: C. Either statement alone is sufficient

Solution

From I: the answer = Yes in every possible case, so I alone is sufficient. From II: the answer = Yes in every possible case, so II alone is sufficient. Answer: Either statement alone is sufficient

Q34.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the length of the rectangle? Statement I: The breadth is 11 cm. Statement II: The length exceeds the breadth by 16 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the length can be 1, 2, 3, 4, ..., so I alone is not sufficient. From II: the length can be 17, 18, 19, 20, ..., so II alone is not sufficient. I and II together: only 27 is possible for the length, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q35.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Ravi, Kiran, Suresh, Divya. Question: Who is the tallest of the four? Statement I: Ravi is the tallest. Statement II: Ravi is taller than Kiran.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the tallest person = Ravi in every possible case, so I alone is sufficient. From II: the tallest person can be Divya, Ravi, Suresh, so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Hard questions

Q36.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Asha, Divya, Suresh, Ravi. Question: Is Divya taller than Ravi? Statement I: Asha is taller than Divya. Statement II: Suresh is taller than Ravi.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: the answer can be Yes (for example order (tallest first): Asha, Divya, Suresh, Ravi) or No (for example order (tallest first): Asha, Suresh, Ravi, Divya), so I alone is not sufficient. From II: the answer can be Yes (for example order (tallest first): Asha, Divya, Suresh, Ravi) or No (for example order (tallest first): Asha, Suresh, Ravi, Divya), so II alone is not sufficient. Even together, the answer can be both Yes and No, so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q37.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Ravi, Divya, Suresh, Meena. Question: Is Suresh taller than Meena? Statement I: Ravi is taller than Divya. Statement II: Meena is shorter than both Ravi and Suresh.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: the answer can be Yes (for example order (tallest first): Ravi, Divya, Suresh, Meena) or No (for example order (tallest first): Ravi, Divya, Meena, Suresh), so I alone is not sufficient. From II: the answer = Yes in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q38.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Ravi, Meena, Kiran, Divya. Question: Who is the tallest of the four? Statement I: Divya is not the tallest. Statement II: Ravi is taller than both Meena and Kiran.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the tallest person can be Kiran, Meena, Ravi, so I alone is not sufficient. From II: the tallest person can be Divya, Ravi, so II alone is not sufficient. I and II together: only Ravi is possible for the tallest person, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q39.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Four people with different heights: Kiran, Suresh, Meena, Divya. Question: Who is the shortest of the four? Statement I: Divya is the shortest. Statement II: Suresh is taller than Meena.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the shortest person = Divya in every possible case, so I alone is sufficient. From II: the shortest person can be Divya, Kiran, Meena, so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Q40.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the area of the rectangle? Statement I: The length and breadth are in the ratio 11:2. Statement II: The perimeter is 26 cm and the length is 11 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: B. Statement II alone is sufficient, but I alone is not

Solution

From I: the area can be 22, 88, 198, so I alone is not sufficient. From II: the area = 22 in every possible case, so II alone is sufficient. Answer: Statement II alone is sufficient, but I alone is not

Q41.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. The sides of the rectangle are whole numbers of cm. Question: What is the area of the rectangle? Statement I: The perimeter is 24 cm. Statement II: The length is 9 cm.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the area can be 11, 20, 27, 32, ..., so I alone is not sufficient. From II: the area can be 9, 18, 27, 36, ..., so II alone is not sufficient. I and II together: only 27 is possible for the area, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q42.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: Is x even? Statement I: x + y = 13. Statement II: x is less than y.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: E. Even both statements together are not sufficient

Solution

From I: the answer can be Yes (for example x = 2, y = 11) or No (for example x = 1, y = 12), so I alone is not sufficient. From II: the answer can be Yes (for example x = 2, y = 3) or No (for example x = 1, y = 2), so II alone is not sufficient. Even together, the answer can be both Yes and No, so the statements are not sufficient. Answer: Even both statements together are not sufficient

Q43.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. x and y are positive integers. Question: Is x even? Statement I: x = 23. Statement II: xy = 299.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: C. Either statement alone is sufficient

Solution

From I: the answer = No in every possible case, so I alone is sufficient. From II: the answer = No in every possible case, so II alone is sufficient. Answer: Either statement alone is sufficient

Q44.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Ages are in whole years. Question: Is Pooja older than Rohit? Statement I: Pooja is 19 years old. Statement II: Rohit is 23 years old.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: D. Both statements together are needed; neither alone is enough

Solution

From I: the answer can be Yes (for example Pooja = 19, Rohit = 1) or No (for example Pooja = 19, Rohit = 19), so I alone is not sufficient. From II: the answer can be Yes (for example Pooja = 24, Rohit = 23) or No (for example Pooja = 1, Rohit = 23), so II alone is not sufficient. I and II together: the answer is always No, so both statements are needed. Answer: Both statements together are needed; neither alone is enough

Q45.

Each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question. Question: Are there more boys than girls in the class? Statement I: Boys are more in number than girls. Statement II: The total number of students is 55.

  1. AStatement I alone is sufficient, but II alone is not
  2. BStatement II alone is sufficient, but I alone is not
  3. CEither statement alone is sufficient
  4. DBoth statements together are needed; neither alone is enough
  5. EEven both statements together are not sufficient
Show answer & solution

Answer: A. Statement I alone is sufficient, but II alone is not

Solution

From I: the answer = Yes in every possible case, so I alone is sufficient. From II: the answer can be Yes (for example boys = 28, girls = 27) or No (for example boys = 1, girls = 54), so II alone is not sufficient. Answer: Statement I alone is sufficient, but II alone is not

Ready to test yourself? 10 fresh Data Sufficiency questions, timed, with solutions at the end.

Start the quiz

Related topics

Number SeriesLetter & Alphabet SeriesCoding-DecodingBlood RelationsDirection SenseSeating ArrangementPuzzlesSyllogismsStatements, Assumptions & ConclusionsAnalogies & Odd One OutClocks & CalendarsRanking & OrderInequalitiesToday's Daily Quiz · 5 questions

Practise this with Sam

A real mock interview, out loud, with an honest scorecard. Free to start.

Start free