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

Given below are two statements based on the following: A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Statement I: Speed of the boat in still water is 12 km per hour. Statement II: Speed of the stream is 4 km per hour. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true but Statement II is false.

  4. Statement I is false but Statement II is true.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 28/v = 7 and 21/u + 21/v = 5. Solving this system yields u = 6 and v = 14. Boat speed = (14+6)/2 = 10 km/hr. Stream speed = (14-6)/2 = 4 km/hr. Statement I (12 km/hr) is false, Statement II (4 km/hr) is true.

Multiple choice

Given below are two statements based on the following: K started a business with Rs. 50,000. After a few months, L joined him with Rs. 30,000. At the end of the year, the total profit was divided between them in the ratio of 2 : 1. Statement I: L joined the business after 2 months. Statement II: The share of the profit would have been 10 : 3, if L had joined after 6 months. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

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

K: 50k for 12 months. L: 30k for x months. Profit ratio = (50*12) / (30*x) = 600 / 30x = 20/x. Given ratio 2:1, so 20/x = 2/1 => x = 10. L joined after 12-10 = 2 months. Statement I is true. If L joined after 6 months, x = 6. Ratio = 600 / (30*6) = 600/180 = 10/3. Statement II is true.

Multiple choice

Directions: The question below is followed by 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. Three friends, Alex, Ben, and Chris, went on a road trip together. During their journey, they tracked the distance they travelled each day and the total distance covered so far. Find the distance each friend travelled on the first and second days. Statement I: The total distance covered by the three friends on the first day was 150 kilometres, and the total distance covered by the three friends on the second day was 240 kilometres. Statement II: Alex and Ben each travelled 45 kilometres on the first day, and Chris travelled 40% more distance than Alex and Ben combined on the second day.

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

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

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

  4. Both the statements together are not sufficient to answer the question.

  5. e
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground. Consider the following two additional pieces of information: I. The dimension of the ground is 80 metres x 50 metres. II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres. Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option.

  1. I alone is sufficient to solve the problem.

  2. II alone is sufficient to solve the problem.

  3. Either of I or II, by itself, is sufficient to solve the problem.

  4. Both I and II are required to solve the problem.

  5. The problem cannot be solved even with both I and II.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: The question given below is followed by two statements labelled I and II. You have to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. P and Q started running around a circular track of 1500 m in opposite directions from same point. How far would Q be from the starting point, when they both met the first time? (I) P took 10 min to run the circular track and Q took half the time taken by P. (II) The ratio of speed of P to that of Q was 1 : 2.

  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 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
C Correct answer
Explanation

To find how far Q is from the start, we need their speeds. Statement I gives P's time (10 min) and Q's time (5 min). We can find speeds. Statement II gives the ratio of speeds directly. Both are sufficient to find the relative speed and the time to meet.

Multiple choice

Directions: The given question is followed by two statements I and II. You have to determine which of the statements is/are necessary/sufficient to answer the question. A bakery sold a total of 5 cakes and 3 pies for \$37.50. What was the price of the 5 cakes? I. If the price of the 5 cakes had been reduced by 15 percent and the price of the 3 pies had been reduced by 10 percent, the total price would have been \$32.50. II. The price of the 5 cakes was $12.50 more than the price of the 3 pies.

  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. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements I and II TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let C be price of 5 cakes, P be price of 3 pies. C + P = 37.50. Statement I: 0.85C + 0.9P = 32.50. This is a system of 2 equations with 2 variables, solvable. Statement II: C = P + 12.50. Substituting into C + P = 37.50 gives P + 12.50 + P = 37.50, also solvable.

Multiple choice

Machine X runs at a constant rate and produces a lot consisting of 100 cans in 2 hours. How much less time would it take to produce the lot of cans if both Machines X and Y were run simultaneously? 1) Both Machines X and Y produce the same number of cans per hour. 2) It takes Machine X twice as long to produce the lot of cans as it takes Machines X and Y running simultaneously to produce the lot.

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

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

  3. Both statements (1) and (2) TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient.

  4. Each statement ALONE is sufficient.

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

Let X be the rate of machine X. Statement 1 says Y = X, so combined rate is 2X. Time taken is half the original time. Statement 2 says time(X+Y) = 0.5 * time(X), which is equivalent to saying the combined rate is twice the rate of X. Both statements are sufficient to determine the time reduction.

Multiple choice

Directions: The question below consists of a question and two statements, labeled (1) and (2), in which certain data is given. Decide whether the data given in the statements is sufficient for answering the question. Using the data provided in the statements and knowledge of mathematics and everyday facts, mark the following: How far is point A from point B? 1. James drove from A to B in 5 hours. 2. When James drove from A to B, his average speed is 50 mph.

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

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

  3. If both statements (1) and (2) 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 statements (1) and (2) together are not sufficient to answer the question and an additional data, that is specific to the problem, is needed
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = Speed * Time. Statement 1 gives time, Statement 2 gives speed. Neither alone gives distance, but together they provide both variables needed.

Multiple choice

A bookstore purchased a set of novels for $240 and later sold the set at a profit. What was the selling price of the novels? (1) The selling price of the set was greater than 125% of the purchase price. (2) The bookstore's profit from the sale was exactly 25% of the selling price.

  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 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): SP > 1.25 * 240 = 300. This doesn't give a specific price. Statement (2): Profit = 0.25 * SP. Since Profit = SP - Cost, SP - 240 = 0.25 * SP. 0.75 * SP = 240. SP = 240 / 0.75 = 320. Statement (2) is sufficient.

Multiple choice

On a certain delivery route, Rafael biked at m miles per hour for 1.5 hours and then at n miles per hour for the next 2.5 hours. What was his average speed, in miles per hour, for the entire trip? (1) 1.5m + 2.5n = 160 (2) n = m + 20

  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 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

Average speed = Total Distance / Total Time. Total Distance = 1.5m + 2.5n. Total Time = 1.5 + 2.5 = 4 hours. Average speed = (1.5m + 2.5n) / 4. Statement (1) gives 1.5m + 2.5n = 160, so average speed = 160 / 4 = 40. Statement (2) relates n and m but does not provide the total distance.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements, labelled (A) and (B), in which certain data is given. You have to decide whether the data given in the statements is sufficient for answering the question. Mark your answer accordingly. A marathon runner running along a prescribed route passes through neighbourhoods J, K, L, M and not necessarily in that order. How long does it take to run from J to M? (A) The runner, at the average runs for 8 km per hour on the route from J to M. (B) M is 4 km from K and 12 km from L, but J is 15 km from K.

  1. The question can be solved using any one of the statements.

  2. The question can be solved using either of the statements.

  3. The question cannot be solved using the given statements.

  4. The question can be solved using both but not either alone.

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

Statement A gives speed but not distance. Statement B gives distances between some points but not the total distance or the specific route order between J and M. Neither statement alone or combined provides enough information to determine the time taken.

Multiple choice

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 or not. What is the value of x? I. (x4)2 = x8 II. (x3)2 = (22)3

  1. Either statement I or II is sufficient.

  2. Both the statements I and II together are sufficient but neither of the statements alone is sufficient.

  3. Each statement alone is sufficient.

  4. Statements I and II together are not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: The question below consists of a question and two statements numbered (1) and (2). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and give answer. By what percent has the price of an overcoat been reduced? (1) The original price was \$380. (2) The original price was \$50 more than the reduced price.

  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

To find the percent reduction, we need the original price and the amount of reduction. Statement 1 gives the original price. Statement 2 gives the reduction amount ($50). Together, we can calculate (50/380)*100.

Multiple choice

Directions: The question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the question. Using the data, mark your answer as What is the value of x4 + y4 if xy = 1? I. x + y = 5 II. x > 0, y > 0

  1. if statement I alone is sufficient to answer the question

  2. if statement II alone is sufficient to answer the question

  3. if both statements I and II are sufficient to answer the question, but neither statement alone is sufficient

  4. if both statements I and II together are not sufficient to answer the question and additional data is required
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given xy=1 and x+y=5. We need x^4 + y^4. x^2 + y^2 = (x+y)^2 - 2xy = 25 - 2 = 23. x^4 + y^4 = (x^2+y^2)^2 - 2(xy)^2 = 23^2 - 2(1)^2 = 529 - 2 = 527. Statement I is 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. Who won the race - the hare or the tortoise? Speed of hare was 80 kmph, but the tortoise was 100 km ahead when they started. (1) The hare finished the race in 6 hours. (2) The speed of hare is 60 kmph more than that of the tortoise.

  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 (1) and (2) together are sufficient, but none of them 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

To determine the winner, we need the time taken by both. Statement 1 gives the hare's time. Statement 2 gives the speed relationship, which allows calculating the tortoise's speed. With both, we can find the distance and time for both to see who finishes first.