Quantitative Aptitude

Data Sufficiency

149 Questions
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Data Sufficiency Questions

Multiple choice

Directions: The following problem has a question and two statements labelled (A) and (B). Use the data given in (A) and (B) to decide whether the statements are sufficient to answer the question. What is its perimeter if the area of a rectangle is 20? (A) The length of the rectangle is 5. (B) The width of the rectangle is 1 unit less than its length.

  1. If the question can be solved using statement (A) alone

  2. If the question can be solved using either or both of the statements

  3. If the question can be solved using statement (B) alone

  4. If the question cannot be solved using the given statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = L * W = 20. (A) L = 5 implies W = 4. Perimeter = 2(5+4) = 18. (B) W = L - 1 implies L(L-1) = 20, which is a quadratic equation L^2 - L - 20 = 0, solving for L gives 5, so W=4. Both statements alone are sufficient.

Multiple choice

Directions: The following problem consists of a question and two statements labelled as (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question. Mark the appropriate choice from (1) to (4). Can we find the value of the eleventh number in a set of eleven numbers, if (1) the average of the first ten numbers in the set is given (2) the average of all the eleven numbers is given

  1. statements (1) and (2) together are not sufficient

  2. statements (1) and (2) taken together are sufficient but neither statement (1) alone nor statement (2) alone is sufficient

  3. statement (1) alone is sufficient, but statement (2) alone is not sufficient

  4. statement (2) alone is sufficient, but statement (1) alone is not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the set be x1, ..., x11. (1) gives the sum of the first 10. (2) gives the sum of all 11. Subtracting the sum of the first 10 from the sum of all 11 gives the 11th number. Both are required.

Multiple choice

Directions: The following problem consists of a question and two statements labelled as (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question. Mark the appropriate choice from (1) to (4). Can we find the relative speed of two trains with respect to each other, if (1) the speed of the first train is 120% more than the speed of the second train (2) the speed of the second train is 80 km/hr

  1. statements (1) and (2) together are not sufficient

  2. statements (1) and (2) taken together are sufficient, but neither statement (1) alone nor statement (2) alone is sufficient

  3. statement (1) alone is sufficient, but statement (2) alone is not sufficient

  4. statement (2) alone is sufficient, but statement (1) alone is not sufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The following questions are accompanied by two statements I and II. You have to determine which statement is/are sufficient to answer the question. A man spends 20 minutes in commuting to his office by bus. How far is the office from his home? I. The bus travels at a speed of 20kmph. II. The same journey by train takes 15 minutes.

  1. If only one statement alone is sufficient to answer the question while the other statement is not sufficient

  2. If either statement I or II is independently sufficient to answer the question.

  3. If neither statement I nor II is sufficient to answer the question.

  4. If both the statements I and II are together sufficient to answer the question.

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I gives speed (20 km/h) and time (20 min = 1/3 h). Distance = Speed * Time = 20 * 1/3 = 6.67 km. Statement II is irrelevant to the distance calculation. Thus, statement I alone is sufficient.

Multiple choice

Directions: The following question consists of three statements A, B and C. You have to determine which of the statements is/are necessary to answer the question. In a military convoy, if truck A followed truck B through a road tunnel that is 1 km long, how many seconds did it take truck A to cross the tunnel? A. Truck A drove into the tunnel exactly 3 seconds after truck B drove into it. B. Truck A drove out exactly 2 seconds after truck B drove out. C. Truck B travelled through the tunnel at a constant speed of 60 km/hr.

  1. Any 2 of them

  2. A and B both

  3. A and B or C

  4. All statements are required.

  5. All even together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the time it takes for truck A to cross the tunnel, we need the speed of truck A and the length of the tunnel. Statement C gives the speed of truck B, and statements A and B provide the relative timing of entry and exit, which allows us to calculate the speed of truck A relative to truck B. All three pieces of information are necessary to determine the specific duration.

Multiple choice

Directions: The following problem consists of a question and three statements numbered I, II and III given below it. You have to decide which of the given statements is/are sufficient to answer the question. Read all the statements and give answer accordingly. How many girls went to see the live cricket match in the stadium? I. The ratio of the number of boys to that of girls who watched the match was 7 : 5. II. If there were 12 more boys, the ratio of the number of the boys to that of girls who watched the match would be 3 : 2. III. The total strength of the stadium is 288. (The total number of boys and girls who went to watch the match was 288.)

  1. I and II only

  2. II and III only

  3. III only

  4. Any of the two statement is sufficient.

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the ratio of boys to girls. Statement III gives the total number of people. With I and III, we can solve for the number of girls. Statement II provides a hypothetical scenario that also allows solving for the initial number of girls when combined with I. Thus, either (I and III) or (I and II) is sufficient.

Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. There are different numbers of students in classes A, B and C. How many are there in class B? I. If 30 students from class A are shifted to class C, then the number of students in class C becomes 180, which is 6 times that in class A. II. If 10 students are shifted from class C to class B, then number of students in both classes becomes the same. III. Ratio of numbers of students in classes C and A is 2 : 1.

  1. Only statements I and III

  2. Only statements II and III

  3. Only statements I and II

  4. Only statement II and either statement I or statement III

  5. All statements together
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From I: A-30 = (C+30)/6. From III: C/A = 2/1. These two allow finding A and C. From II: C-10 = B+10. With C known from I and III, B can be found. Thus I and II are sufficient (or I, II, III). The question asks for the minimum sufficient set, which is I and II.

Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. How many students are there in the group? I. Average age of the students in the group is 10 years. II. If a new student of age 4 years is added to the group, then the average age becomes 9 years. III. Three students in the group are 12 years of age, two of the students in the group are 7 years of age.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statement II and either statement I or statement III

  4. All three statements

  5. None of the statements
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let n be the number of students and S be the sum of their ages. I: S/n = 10, so S = 10n. II: (S + 4)/(n + 1) = 9, so S + 4 = 9n + 9. Substituting S = 10n: 10n + 4 = 9n + 9, so n = 5. Statements I and II are sufficient.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. There are 8 persons of ages y, x, 35, p, 25, q, 27, 29 (in years). What is their average age? I. x is 6 years more than p, which is 5 years less than q. II. y is 4 years less than q. III. x is 15 years more than y.

  1. Only statements I and II

  2. Only statements I and III

  3. None of the statements

  4. All three statements

  5. Any two statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We have 8 variables: y, x, 35, p, 25, q, 27, 29. We need the sum of these to find the average. The statements provide relations between x, p, q, and y, but they do not provide enough absolute values to determine the sum of all 8 ages.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. At what speed can the man swim in still water? I. The man can swim 15 km downstream in 3 hours. II. He can swim 5 km upstream in 5 hours. III. Speed of the man is 50% more than the speed of current.

  1. Only statements I and II

  2. Only statements II and III

  3. Any two statements

  4. All three statements

  5. Only statement III and either statement I or statement II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let m be man's speed and c be current speed. I: m+c = 15/3 = 5. II: m-c = 5/5 = 1. III: m = 1.5c. With any two statements, we have two equations with two variables, which is sufficient to solve for m.

Multiple choice

Directions: The question given below is followed by some information given in three statements I, II and III. You have to consider the information in all the three statements and decide the information in which statement is not required to answer the question and therefore, can be dispensed with. What will be the speed of the boat in still water? I. The boat covers 24 km in 4 hours in downstream. II. In still water, the speed of the boat is thrice the speed of the stream. III. The boat covers 24 km in 8 hours in upstream.

  1. Either I or II

  2. Either II or III

  3. Either I or III

  4. Any one statement

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the speed of the boat in still water (b) and stream (s), we need both downstream (b+s) and upstream (b-s) speeds. Statement I gives b+s, and Statement III gives b-s. Statement II is redundant because b and s can be found using I and III alone.

Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the radius of the circular track? I. An athlete makes a complete round the track in 1 hr 40 min. II. The average speed of the athlete is 25 kmph.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the radius, we need the circumference (C = speed * time). Statement I gives time, Statement II gives speed. Both are needed to calculate the total distance (circumference), from which the radius can be derived (C = 2*pi*r).

Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the speed of the lorry? I. A man driving his car at the speed of 50 kmph observes that a lorry, travelling in opposite direction, takes 100 seconds to pass him. II. The lorry crosses a pole in 8 seconds and a 260-m long bridge in 10 seconds.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives relative speed (Lorry speed + 50 kmph) = Length / 100s. We don't know the length of the lorry, so we cannot find the speed. Statement II: Lorry crosses a pole in 8s (L = 8v) and a 260m bridge in 10s (L + 260 = 10v). Substituting L gives 8v + 260 = 10v, so 2v = 260, v = 130 m/s. Statement II is sufficient.

Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the time taken by the student to reach his school by bus? I. If the speed of the bus is increased by 10%, he can reach 15 minutes early. II. If the speed of the bus is decreased by 20%, he will reach 40 minutes late.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer