Quantitative Aptitude

Data Sufficiency

149 Questions
All Time, Speed & Distance 69 Algebraic Equation Solving 18 Averages & Mixtures 18 Percentage Problems 9 Profit, Loss & Discount 9 Time & Work Efficiency 9 Ratio & Proportion 8 Geometry & Mensuration 7 Basic Trigonometry 1 Simple & Compound Interest 1

Data Sufficiency Questions

Multiple choice

Directions: The following problem consists of a question and two statements which are labelled (1) and (2). Use the data given in statements (1) and (2) together with other available information (such as the numbers in a day, the definition of clockwise, mathematical facts, etc.) to decide whether the statements are sufficient to answer the question. Mark your answer accordingly. In 1990, the ratio of Maruti cars sold to other brand cars sold was 4 to 1. How many other brand cars were sold in 1990? (1) 60,00,000 Maruti cars were sold in 1990. (2) A total of 75,00,000 cars were sold in 1990.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question.

  3. Both statements (1) and (2) together are sufficient to answer the question, although neither statement alone is sufficient.

  4. Either statement (1) alone or statement (2) alone is sufficient.

  5. Statements (1) and (2) together are not sufficient to answer the question, and additional data relevant to the problem is needed.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratio of Maruti to other cars is 4:1. Statement (1) gives the number of Maruti cars (4x = 60,00,000), allowing us to find x. Statement (2) gives the total (5x = 75,00,000), also allowing us to find x. Thus, either statement is sufficient.

Multiple choice

Directions: The given problem consists of a question and two Statements I and II. Decide whether the data provided in the statements are sufficient to answer the question. Mark answer as (1) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question. (2) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question. (3) if the data in both Statements I and II are required to answer the question. (4) if the data in both Statements I and II together are not sufficient to answer the question. There were 90 students to be interviewed for selection to a computer course. To finish the interview in one day three panels X, Y and Z were formed. How many students were interviewed by Panel X? I. The three panels on an average interview 30 students. II. The number of students interviewed by Panel X is more by 4 than the students interviewed by Panel Z. The number of students interviewed by Panel Y is more by 2 than the students interviewed by Panel Z.

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I only restates that the total number of students is 90, which is already given in the problem. Statement II provides two equations relating X, Y, and Z to each other, which, when combined with the total of 90, allows us to solve for the exact number of students interviewed by Panel X. Thus, Statement II alone is sufficient.

Multiple choice

Directions: The question given below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. Two boats A and B, 240 km apart, start moving towards each other from the ends X and Y going upstream and downstream, respectively. If the speed of the flow of water in the stream is 4 km/h, after how much time will both the boats cross each other? (I) The ratio of the speeds of the boats while going upstream and downstream is 2 : 3, respectively. (II) Speeds of the both the boats are equal.

  1. The question can be answered using statement I alone but cannot be answered using the other statement alone.

  2. The question can be answered using statement II alone but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both the statements together but cannot be answered using either of the statements alone.

  5. The question cannot be answered even using both the statements together.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: In the following problem, a question is followed by two statements (A) and (B). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. The value of a piece of land is increasing every year by 10%, starting from 1990. What is its value in 1996? (A) Value of the land in 1990 was Rs. 1 lakh. (B) Value of the land in 1994 was Rs. 1,46,410.

  1. Statement (A) alone is sufficient but statement (B) alone is not.

  2. Statement (B) alone is sufficient but statement (A) alone is not.

  3. Both statements (A) and (B) together are sufficient but none of them alone is sufficient.

  4. Both statements are sufficient independently.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement (A) gives the base value, allowing calculation of the value in 1996 using compound interest. Statement (B) gives the value in 1994, which can be used to find the value in 1996 by multiplying by 1.1 twice. Both statements are sufficient independently.

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer - A man sells mobile sets at a profit of 20%. How much total amount does he gain in profit? (I) He sells 20 mobile sets (II) He sells each mobile set for Rs. 18000

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If both statements together are sufficient, but neither statement alone is sufficient.

  4. If each statement alone (either I or II) is sufficient.

  5. If statements I and II together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives quantity (20 sets) but not cost per set. Statement II gives selling price per set (Rs. 18000) but not quantity. Profit = 20% means profit amount = 0.2 × selling price. Total profit = profit per set × number of sets. Neither alone gives total profit: I lacks price, II lacks quantity. Together: profit per set = 0.2 × 18000 = Rs. 3600, total profit = 3600 × 20 = Rs. 72000. Both are needed, so C is correct.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the time taken by Raj from point A to other point B? I. If he walks 25% faster than his usual speed then he reaches 20 seconds earlier. II. If he walks half of his usual speed he takes 100 seconds more to reach the finishing point B.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If both statements I and II together are sufficient, but neither statement alone is sufficient.

  4. If each statement alone (either I or II) is sufficient.

  5. If statement I and II together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let usual speed = v and time = t. Distance = v × t. From I: 1.25v = d/(t-20) → two equations, two unknowns → solvable for t. From II: 0.5v = d/(t+100) → also solvable. Each statement alone gives sufficient data to find the time.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Is value of y more than 1? (I) Value of y is more than 0. $(II) (y^2 - 4 > 0)$

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I only tells us y > 0, which means y could be 0.5 or 5. Statement II (y² - 4 > 0) implies y > 2 or y < -2, but alone doesn't confirm y > 1 since y could be -3. Together, if y > 0 and (y > 2 or y < -2), then y must be > 2, which definitely means y > 1.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? The company earned how much profit in the years 2002? (A) In 2001 the company earned 40% more profit which earned in the year 2003. (B) The company earned the profit of 20 crores together in the year 2001 and 2002. (C) The company earned in 2003, 80% profit which was earned in the year 2002.

  1. Any two

  2. Either A and B or B and C are sufficient.

  3. A and B or C are sufficient

  4. A,B and C all the three are necessary to answer

  5. A,B and C together are not sufficient to answer
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need profit in 2002. Let profit in 2002 = P. From (C): Profit in 2003 = 0.8P. From (A): Profit in 2001 = 1.4 × (0.8P) = 1.12P. From (B): Profit in 2001 + Profit in 2002 = 20 crores, so 1.12P + P = 20. Therefore 2.12P = 20, giving P = 20/2.12 crores. All three statements are necessary - (B) gives total, (A) and (C) relate 2001 and 2003 to 2002.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? The marks obtained by Ankit in English is 15 more than his average marks in English, Maths, Geography and Science. How many marks did he get in Science? I. He got total 120 marks in English and Science. II. The difference between his marks in Geography and Maths is 120.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let E, M, G, S be marks in English, Maths, Geography, Science. Given: E = (E+M+G+S)/4 + 15, which simplifies to 3E = M + G + S + 60. Statement I: E + S = 120, giving S = 120 - E. Substituting: 3E = M + G + 120 - E + 60, or 4E = M + G + 180. Two unknowns remain. Statement II: |G - M| = 120. Even with both statements, we cannot uniquely determine M and G (could be M=0, G=120 or M=120, G=0 or many other combinations). Thus, data is insufficient.

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What percent marks did Deepa get in a test of 4 subjects? (I) She got 83 marks in physics and 80 marks in English. (II) She got 95 marks in Maths and 72 marks in Chemistry.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find percentage, we need obtained marks and total maximum marks. Statement I gives marks in Physics (83) and English (80). Statement II gives marks in Maths (95) and Chemistry (72). We have obtained marks for all 4 subjects, but we don't know the maximum marks for each subject. Without knowing total possible marks, percentage cannot be calculated. Thus both statements together are insufficient.

Multiple choice

The question given below contains two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question In a class the average age of 22 students and a teacher is 20 years. What is the age of the teacher. I. The teacher's age is 25 years more than the age of the eldest student. II. The average age of the 19 students without the teacher is 16 years.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 22 students + 1 teacher = 23 × 20 = 460 years. From I: Teacher = Eldest student + 25. From II: Average of 19 students (without teacher) is 16 years, so their sum = 19 × 16 = 304. But we don't know which 19 students these are or how they relate to the eldest student. Combining both statements doesn't give a unique solution since we don't know the age of the eldest student or which students are included in statement II. The answer key is correct.

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. How many girls are there in the class? I. Reena is 9th from the left and 7th from the right. II. Ratio of Boys and Girls in the class is 1 : 2.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient

  3. If each statement alone (either I or II) is sufficient

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I alone is insufficient: Reena's position (9th left, 7th right) tells us total students = 15, but not how many are girls. Statement II alone is insufficient: The 1:2 ratio alone doesn't give the actual count. Together they are sufficient: Total = 15, ratio 1:2 means girls = (2/3) × 15 = 10.

Multiple choice

A boat will take how much time to cross the river against the stream of the river? A. In still water the speed of the boat is 15 km/hr. B. The width of the river is 8 km. C. The speed of the stream is 2 km/hr.

  1. Only A

  2. Only B

  3. Only C

  4. All A, B and C are required to answer the question.

  5. A, B and C are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Time = distance / speed. Against stream: effective speed = boat speed - stream speed. Statement A gives boat speed (15 km/hr). Statement C gives stream speed (2 km/hr). So effective speed = 15 - 2 = 13 km/hr. Statement B gives distance (8 km). Time = 8/13 hours. All three statements are required; none alone gives the time.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer - $What is accurate average of (n), 35, 39, 42, (p) and (w)? (I) (n) is six more than (w). (II) (w) is four less than (p).$

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient

  5. both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need average of n, 35, 39, 42, p, w = (n + 35 + 39 + 42 + p + w)/6 = (n + p + w + 116)/6. Statement I: n = w + 6. Statement II: w = p - 4. Even with both statements, we have 3 unknowns (n, p, w) with only 2 equations. We cannot find n + p + w uniquely, so average cannot be determined. Both statements together are insufficient.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer What is Nandita's share in the profit of Rs. 21,000 to be distributed between her brother and her? (I) Nandita invested Rs. 50,000. (II) Amount invested by Nandita is 40% of the amount invested by her brother.

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient.

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find Nandita's share, we need profit distribution ratio. Statement I gives Nandita's investment (Rs. 50,000) but not her brother's. Statement II says Nandita's investment is 40% of her brother's, so brother invested 50,000/0.4 = 125,000. Ratio = 50,000:125,000 = 2:5. Neither alone is sufficient; together they give the ratio to calculate Nandita's share = (2/7)×21,000 = Rs. 6,000.