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 has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

A worker was hired for 5 days. What was her average daily wage for 5 days? (1) She was paid a total of Rs. 500 for 5 days. (2) She earned Rs. 100 the first day and Rs. 100 the last day.

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

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

Correct option is (1).

Multiple choice

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

Find the value of x. (1) x + y = 6 (2) 2x – 2y = 12

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Correct option is (3).

Multiple choice

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

A dozen eggs cost Rs. 9 in January 1990. Did a dozen eggs cost more than Rs. 9 in January 1991? (1) In January 1990, the average worker had to work 5 minutes to pay for a dozen eggs. (2) In January 1991, the average worker had to work 4 minutes to pay for a dozen eggs.

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Correct option is (5).

Multiple choice

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

A plane flies over New Delhi. What is its speed in km per hour?

(1) The plane is flying in a circle. (2) The plane is flying at the speed of 1/9 km per second.

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In statement (1), no information is given regarding the speed of the plane. From statement (2), it is given that in 1 second, the plane covers = 1/9 km. So, in 3600 seconds, the plane covers = 400 km. This implies that the speed of the plane is 400 km/hr. So, the correct option is (2).

Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: What is the average of 5 numbers in AP? (1) The first term is 3 and is 2 less than the next term. (2) The third term is 7.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but none of them alone is sufficient

  4. if both statements are sufficient independently

  5. if both (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For 5 numbers in AP, the average is the middle term (3rd term). Statement (1): a = 3, a+d = 3+2 = 5, so d=2. The 3rd term is a+2d = 3+4 = 7. The average is 7. Statement (2): 3rd term is 7. The average is 7. Both are sufficient.

Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: What is the speed of a jeep? (1) The jeep is faster than a Car by 10 km/h. (2) The car took two hours more than the jeep to cover 100 km.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but none of them alone is sufficient

  4. if both independently are sufficient

  5. if both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of car be v, jeep be v+10. (100/v) - (100/(v+10)) = 2. This equation allows solving for v. Neither statement alone provides enough info to solve for v without the other.

Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75? (1) None of the six numbers is less than 75. (2) None of the six numbers is greater than 75.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but neither of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the average of 6 numbers is 75, their sum is 450. If no number is less than 75 (Statement 1), the only way the sum can be 450 is if all are 75. Similarly, if no number is greater than 75 (Statement 2), all must be 75. Both statements independently force all numbers to be 75.

Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: What was Janet's score in the fourth physics test? (1) Her score in the fourth test was 12 points higher than her average (arithmetic mean) score in the first three tests. (2) Her score in the fourth test raised her average (arithmetic mean) test score from 87 to 90.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement (2) is sufficient: Let S3 be the sum of the first 3 tests. S3/3 = 87, so S3 = 261. Let x be the 4th test score. (261 + x)/4 = 90, so 261 + x = 360, x = 99. Statement (1) is not sufficient because it relates the score to the average, but the average is unknown.

Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: How many hours does it take 12 machines with identical production rates, running simultaneously without stopping, to fill a certain production order? (1) It takes each machine, running alone continuously, 60 hours to fill the production order. (2) It takes 10 of these machines, running simultaneously without stopping, 6 hours to fill the production order.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement (1) gives the rate of one machine (1/60 per hour). 12 machines together have a rate of 12/60 = 1/5 per hour, so time = 5 hours. Statement (2) says 10 machines take 6 hours, so 1 machine takes 60 hours, which is consistent with (1). Both are sufficient.

Multiple choice

Directions: The following question is accompanied by statements A, B and C. You have to determine the statement(s) which is/are sufficient to answer the question. What is the amount of work done by A, B, C and D in an hour? A. A, who can complete 50% of the total work in 10 hours, is 30% more efficient than B. B. B is 50% more efficient than C and 20% more efficient than D. C.The ratio of efficiency of B, C and D is 5 : 7 : 8.

  1. Only C alone is sufficient

  2. Only A and B together are sufficient

  3. Only A and C together are sufficient

  4. Only A and either B or C together are sufficient

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

Statement A gives A's efficiency relative to B. Statement B gives B's efficiency relative to C and D. Statement C gives the ratio of B, C, and D. To find the total work done by A, B, C, and D in an hour, we need the absolute work rate of at least one person, which is provided by A. Combining A with either B or C allows us to determine the rates of all four.

Multiple choice

Directions: In this problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. At what price did Anju purchase the watch, which she sold to Ankush? I. Anju sold her watch to Ankush at 20% profit. II. Ankush sold the watch to Ritika at 10% loss, who paid Rs. 12 more than Anju did for buying that watch. III. Anju could have gained Rs. 15 more if she had sold it at a profit of 30%.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statements II and III

  4. Either statements I and II or statements I and III

  5. All three statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the cost price for Anju be x. Statement I gives the selling price as 1.2x. Statement II relates the selling price to Ritika's cost, allowing us to solve for x. Statement III provides a direct equation to solve for x independently. Thus, either I and II or I and III are sufficient.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream? (1) At the picnic, 60 percent of the guests were served a double scoop of ice-cream. (2) A total of 120 scoops of ice-cream were served to all the guests at the picnic.

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

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

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives the percentage but not the total number of guests. Statement (2) gives the total scoops but not the distribution (single vs double). Together, if N is the total guests, 0.6N * 2 + 0.4N * 1 = 120, which simplifies to 1.6N = 120, allowing us to solve for N and then the number of double scoops.

Multiple choice

Directions: The following problem contains a question and two statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question and then mark the option accordingly. All trainees in a certain aviator-training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests? (A) 10 percent of the trainees did not pass either test. (B) 20 percent of the trainees passed only the flight test.

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

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

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

  4. Both statements independently are sufficient.

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

Let W=70, F=80. Total = 100. (A) 10% pass neither, so 90% pass at least one. W+F - Both = 90 => 70+80 - Both = 90 => Both = 60. (B) 20% pass only flight, so 80 - Both = 20 => Both = 60. Both are sufficient.

Multiple choice

Directions: The following problem contains a question and two statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question and then mark the option accordingly. If a certain animated cartoon consists of a total of 17,280 frames on film, how many minutes will it take to run the cartoon? (A) The cartoon runs without interruption at the rate of 24 frames per second. (B) It takes 6 times as long to run the cartoon as it takes to rewind the film, and it takes a total of 14 minutes to do both.

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

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

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

  4. Both statements independently are sufficient.

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

Statement A gives the frame rate, allowing calculation of time (17280 / 24 = 720 seconds = 12 minutes). Statement B provides a system of equations (Run = 6 * Rewind, Run + Rewind = 14) which also allows solving for the run time. Both are sufficient independently.

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 statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer according to the following codes: (a) If the question can be answered by using statement I alone but cannot be answered by using statement II alone. (b) If the question can be answered by using statement II alone but cannot be answered by using statement I alone. (c) If both statements I and II together are required to answer the question. (d) If the answer can be found by using any of the two statements alone. (e) If both the statements together are not sufficient to answer the question. A cart with front wheel smaller than rear wheel moves a distance of 800 ft. Find the revolutions made by the front wheel. I. The circumference of the front wheel is 25 ft and that of the rear wheel is 32 ft, which makes 7 more revolutions than that by the rear wheel. II. The circumference of the front wheel is 7 less than that of the rear wheel and makes 7 revolutions more than those made by the rear wheel.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
A Correct answer