Quantitative Aptitude

Data Sufficiency

149 Questions
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Data Sufficiency Questions

Multiple choice

Directions: The following question is accompanied by two statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. The present age of P is 20% less than the present age of Q and the present age of R is 20% more than the present age of Q. The present age of S is 20% less than the present age of R and the present age of T is 5/3 than the present age of S. Find the age of Q after 7 years. (A) The average of the present ages of P, Q and R together is 25 years. (B) The average of the present ages of P, Q, R, S and T together is 27.8 years.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

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

Let Q's present age be q. Then P = 0.8q and R = 1.2q, so their average is q, making statement A sufficient. The five-age sum is 5.56q, so statement B also determines q, making either statement sufficient.

Multiple choice

Lily and Rose are running around a circular track in opposite directions. After how much time do they meet, if they start simultaneously from the same point? (1) Their speeds are 6.0 miles/hour and 4.5 miles/hour, respectively. (2) If the diameter of the track is exactly double the present diameter, it takes 4 minutes for them to meet.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 6.0 + 4.5 = 10.5 mph. Time to meet = Distance / Relative Speed. Statement 1 gives speeds but no distance. Statement 2 gives a relationship between diameter and time, which allows calculating the distance (circumference). Thus, statement 2 is sufficient.

Multiple choice

George went on a round trip from New Jersey to New York. While going from New Jersey to New York, he drove at an average speed of 70 miles per hour. He started his journey back on the same route, and due to rush hours his speed was slow. What was the average speed of George during his entire round trip? (1) It took one and a half hours for George to travel from New Jersey to New York. (2) While going from New York to New Jersey, he drove at a constant speed of 49 miles per hour.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed for a round trip is 2 * v1 * v2 / (v1 + v2). Statement 1 gives time but not return speed, so it is insufficient. Statement 2 provides the return speed (49 mph), which allows calculation of the average speed using the formula, making it sufficient.

Multiple choice

Directions: The following 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. What is the value of a3 + b3? (1) ab = 12 (2) a + b = 7

  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 together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

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

The expression a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2). Since a^2 + b^2 = (a + b)^2 - 2ab, we can rewrite the expression as (a + b)((a + b)^2 - 3ab). Knowing both a + b and ab allows us to calculate the value, so both statements are required.

Multiple choice

Directions: The following 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. What is the value of (z - 21)? (1) z2 - 441 = 0 (2) (2z - 42)2 = 0

  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 together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

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

Statement (1) z^2 - 441 = 0 implies z^2 = 441, so z = 21 or z = -21. Thus (z - 21) could be 0 or -42. Statement (2) (2z - 42)^2 = 0 implies 2z - 42 = 0, so 2z = 42, z = 21. Thus (z - 21) = 0. Statement (2) is sufficient.

Multiple choice

Directions: The following 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. Find the value of 4 consecutive numbers. (1) The sum of the first two numbers is 4 more than the third number. (2) The smallest number is a prime number.

  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 together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

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

Let the numbers be x, x+1, x+2, x+3. (1) x + (x+1) = (x+2) + 4 => 2x + 1 = x + 6 => x = 5. The numbers are 5, 6, 7, 8. (2) Smallest is prime. 5 is prime, so this is consistent. Statement 1 is sufficient.

Multiple choice

Directions: The following 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. Amelia noted the time taken by her to complete 1 mile race in 4 different attempts. The duration of time comes out to be a multiple of same number h such as 2h, 4h, 5h, h. Was the average of the 4 durations less than 6? (1) h > 3 (2) h < 2

  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 together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

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

The durations are 2h, 4h, 5h, and h. The average is (2h+4h+5h+h)/4 = 12h/4 = 3h. We want to know if 3h < 6, which is equivalent to h < 2. Statement (1) says h > 3, which is not sufficient. Statement (2) says h < 2, which directly answers the question.

Multiple choice

Directions: The following 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. If xy = z, what is the value of x? (1) y = 4z (2) y2 = 16

  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 together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Statement I: A cyclist is moving on an unbanked road with a speed of 7 km/h and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s2) Statement II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2 m radius with the speed of 18.5 km/h without slipping. In the light of the above statements, choose the correct answer from the options given below.

  1. Statement I is incorrect and statement II is correct.

  2. Statement I is correct and statement II is incorrect.

  3. Both statement I and statement II are incorrect.

  4. Both statement I and statement II are correct.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For Statement I, the maximum speed without slipping on an unbanked road is sqrt(mu * g * r) = sqrt(0.2 * 9.8 * 2) = 1.98 m/s, which is greater than the cyclist's speed of 1.94 m/s, so they will not slip. For Statement II, the safe speed range on a banked road with friction includes 18.5 km/h, meaning both statements are correct.

Multiple choice

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: Is the speed of the boat in still water at least twice that of the speed of the stream? Statement I : The time taken by the boat to reach a point P, from Q is exactly twice the time taken by the boat, to reach Q from the point P. Statement II : The time taken by the boat to cover 8 km downstream is 40 minutes and it takes four hours to cover 16 km upstream.

  1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I implies the speed of the boat (b) and stream (s) satisfy (b-s) = 0.5(b+s), which simplifies to 2b - 2s = b + s, or b = 3s. This confirms b >= 2s. Statement II provides specific values to calculate b and s directly, which also confirms the condition. Since both statements independently provide enough information, C is correct.

Multiple choice

How much time will the bus take to go from Denver to Nebraska? 1. If the bus increases the speed by 15%, it will reach there in 6 hours. 2. The speed of the bus is more than 40 miles per hour.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement 1 gives a relationship between speed and time (if speed increases by 15%, time is 6 hours). This allows solving for the original time. Statement 2 only provides a lower bound on speed, which is insufficient to determine the exact time.

Multiple choice

Drake played a game with his friends where he had to think of a number. Considering his number to be 'a', determine the value of 'a'. Statement 1: 6(8 – a) = 0 Statement 2: a4 = 4,096

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement 1: 6(8-a) = 0 implies a = 8. Sufficient. Statement 2: a^4 = 4096 implies a = 8 or -8. Not sufficient. Thus, statement 1 alone is sufficient.

Multiple choice

A turtle is crossing a field, how many meters total did he pass?(1) The average speed of the turtle is 2 meters per minute.(2) Had the turtle walked 1 meter per minute faster than his average speed it would have finished the same path 40 minutes earlier.

  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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed be v and distance be d. (1) v = 2. (2) d/(v+1) = d/v - 40/60. With both, we can solve for d. Neither alone is sufficient because (1) lacks time and (2) lacks the specific speed.

Multiple choice

Mr. David usually starts at 9:00AM and reaches his office just in time, driving at his regular speed. Last Wednesday, he started at 9:30AM and drove 25% faster than his regular speed. Did he reach the office in time? (1) Last Monday, he started to his office 20 minutes early, drove 20% slower than his regular speed, and reached his office just in time. (2) Last Tuesday, he started to his office 10 minutes early, and reached the office 10 minutes early driving at his regular speed.

  1. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

  2. if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient.

  3. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

  4. if EACH statement ALONE is sufficient to answer the question;

  5. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let d be distance, r be regular speed. Time taken = d/r. Statement (1) provides a scenario with a different time and speed that allows solving for the relationship between d and r, which is sufficient to determine if he reached on time in the Wednesday scenario. Statement (2) only provides information about his regular speed behavior, which is insufficient to determine the outcome of the Wednesday scenario.

Multiple choice

Directions: The item given below consists of a question and two statements, numbered I and II. You have to decide whether the data provided in the statement is sufficient to answer the question. Read both the statements and choose the correct option. What is the time taken by pipe C to fill the water tank alone if the time taken by pipe A to fill the water tank is 12 minutes? I. Time taken by pipes A, B and C to fill the water tank together is 6 minutes. II. The ratio of speed of water that comes through pipe B to that of the water that comes out of pipe C is 4 : 3.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both statement I and II together is necessary to answer the question.

  5. The data even in both statements I and II together is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the combined rate (A+B+C). Statement II gives the ratio of rates for B and C. With A known, we have two equations with two variables (B and C), allowing us to solve for C.