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

In a kilometer race, by how many meters Chandu beats Chand? Statement I : In a kilometer race, Chandu beats Chandan by 100 meters. Statement II : The respective ratio of the speed of Chandan and Chand is 4: 3. Statement III : In a kilometer race, Chandan beats Chand by 150 meters.

  1. III or (I and II together) are sufficient

  2. Only III is sufficient.

  3. Only I and (II or III) together are sufficient.

  4. Only statement I, II, and III together are sufficient.

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

Statement I tells us Chandu beats Chandan by 100m. Statement III tells us Chandan beats Chand by 150m. Combining these: Chandu covers 1000m while Chandan covers 900m, and Chandan covers 1000m while Chand covers 850m. In the same time, Chandu's distance to Chand's distance ratio is 1000:850 = 20:17. When Chandu runs 1000m, Chand runs (17/20)*1000 = 850m. So Chandu beats Chand by 150m. Statement I alone is insufficient, Statement III alone is insufficient, but I+III together are sufficient. Statement II (ratio 4:3) is not needed.

Multiple choice

In each of the following questions, a question is followed by some statements. Read the statements and decide which statements are necessary to answer the question. निम्नलिखित में से प्रत्येक प्रश्न में, प्रश्न के पश्चात कुछ कथन दिए गए है। कथनों को पढ़ें और यह निर्णय लें कि प्रश्न का उत्तर देने के लिए कौन से कथन आवश्यक हैं। What is the speed of man in still water? I: The speed of man in still water is three times the speed of the stream. II: In 20 minutes, the man can swim 5 Km with the stream whereas he can swim only 2.5 Km against the stream in same time. शांत जल में आदमी की गति क्या है? I: शांत जल में आदमी की गति धारा की गति की तीन गुना है। II: 20 मिनट में, आदमी धारा के साथ 5 किमी. की दूरी तय कर सकता है जबकि धारा की विपरीत दिशा वह केवल 2.5 किमी. की दूरी तय कर सकता है।

  1. Only I केवल I

  2. Only II केवल II

  3. Any one of the two दोनों में से कोई भी

  4. All together are sufficient सभी एक साथ पर्याप्त हैं

  5. All together are not sufficient सभी एक साथ भी पर्याप्त नहीं हैं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II alone is sufficient. From the distances: downstream speed = 5 km in 20 minutes = 15 km/h; upstream speed = 2.5 km in 20 minutes = 7.5 km/h. Speed in still water = (downstream + upstream)/2 = (15 + 7.5)/2 = 11.25 km/h. Statement I relates still water speed to stream speed but doesn't give numerical values. Only II is needed.

Multiple choice

For each of the following questions two statements are given. Use the data of those statements and then determine which of the following statements is necessary to answer the question. What is the total investment made by three partners - A, B and C? I: A invested Rs 2000. The ratio of time for A, B and C is 1:2:3. II: The total profit is Rs 6000.

  1. Statement I is sufficient to answer the question.

  2. Statement II is sufficient to answer the question.

  3. Either Statement I or statement II is sufficient to answer the question.

  4. Neither Statement I nor statement II is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives A's investment and time ratios but no profit or B and C's investments. Statement II only gives total profit. We need profit AND the ratio of investments (or B and C's investment amounts) to find total investment. Neither alone is sufficient.

Multiple choice

Find the time taken by the boat to cover 81.6 Km downstream and 70 Km upstream. I. Speed of the boat in still water is 250% more than the speed of the stream. II. Sum of the twice the speed of the boat in still water and thrice the speed of the stream is 40 Km/h III. Upstream speed of the boat is 10 Km/h.

  1. All I, II and III

  2. Any two of the three

  3. Only I and III

  4. Any one of the three

  5. Even I, II and III together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed = b, stream speed = s. We need downstream and upstream times. From I: b = s + 2.5s = 3.5s. From II: 2b + 3s = 40. From III: b - s = 10. Any pair works: I+III: b = 3.5s and b - s = 10 gives 2.5s = 10, s = 4, b = 14. II+III: 2b + 3s = 40 and b = s + 10 gives 2(s+10) + 3s = 40, 5s = 20, s = 4, b = 14. I+II: b = 3.5s and 2b + 3s = 40 gives 7s + 3s = 40, s = 4, b = 14. All pairs yield same result.

Multiple choice

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip? (1) The trip was 460 miles long and took 4 hours to complete. (2) The train traveled at an average rate of 115 miles per hour on the trip.

  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
E Correct answer
Explanation

Statement 1 gives total distance and time, but not the speed at the halfway point. Statement 2 gives the average speed for the whole trip, which does not define the speed at the halfway point. Even together, they do not provide information about the speed at a specific point in the trip.

Multiple choice

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the speed of the boat in still water? I. The speed downstream is 12 kmph. II. The speed upstream is 4 kmph. III. In a to and fro journey between two points, the average speed of the boat was 6 kmph.

  1. I and II only

  2. All I, II and III

  3. III, and either I or II

  4. Any two of the three

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

Let boat speed be b and stream speed be s. I: b+s = 12. II: b-s = 4. III: Average speed = 2(b+s)(b-s) / (b+s + b-s) = 2(b^2-s^2) / 2b = (b^2-s^2)/b = 6. Any two statements allow solving for b and s.

Multiple choice

Two cars pass each other in opposite direction. How long would they take to be 500 km apart? I. The sum of their speeds is 135 km/hr. II. The difference of their speed is 25 km/hr.

  1. I alone sufficient while II alone not sufficient to answer

  2. II alone sufficient while I alone not sufficient to answer

  3. Either I or II alone sufficient to answer

  4. Both I and II are not sufficient to answer

  5. Both I and II are necessary to answer
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relative speed = speed1 + speed2. Distance = 500 km. Time = Distance / Relative Speed. Statement I gives the sum of speeds directly, so time = 500 / 135. Statement II gives the difference, which is not enough to find the sum.

Multiple choice

How much time did X take to reach the destination? I. The ratio between the speed of X and Y is 3 : 4. II. Y takes 36 minutes to reach the same destination.

  1. I alone sufficient while II alone not sufficient to answer

  2. II alone sufficient while I alone not sufficient to answer

  3. Either I or II alone sufficient to answer

  4. Both I and II are not sufficient to answer

  5. Both I and II are necessary to answer
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Speed ratio X:Y = 3:4. Time ratio X:Y = 4:3. If Y takes 36 minutes, X takes (4/3) * 36 = 48 minutes. Both statements are required to establish the relationship and the specific value.

Multiple choice

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide which of the statements, if any, is/are sufficient to answer the given question. What is the value of x? (1) x/y = 3 (2) x – y = 9

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

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

  3. Statements (1) and (2) together are sufficient to answer the question, but none of them alone is sufficient to answer the question.

  4. Either statement (1) alone or statement (2) alone is sufficient to answer the question.

  5. Neither statement (1) nor statement (2) is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives x/y = 3, so x = 3y. Statement (2) gives x - y = 9. Substituting (1) into (2) gives 3y - y = 9, 2y = 9, y = 4.5, x = 13.5. Neither statement alone provides a unique value for x.

Multiple choice

Directions: The problem below consists of a question and two statements labelled (A) and (B) given below it. Read them carefully and decide which of the given statements is/are sufficient to answer the question. Choose the correct option accordingly. What is the value of x + y? (A) x – y = 4 (B) 3x + 3y = 4

  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 statements (A) and (B) together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (A) and (B) together are not sufficient and additional data is needed.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement (A) is x - y = 4. Statement (B) is 3x + 3y = 4, which simplifies to x + y = 4/3. Statement (B) directly gives the value of x + y, while (A) does not.

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. Find the value of z if x = 3. (1) z = (x + 3)4 (2) z = 2x + y Mark your answer as:

  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

  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 additional data is required
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (1) gives z = (3+3)^4 = 6^4 = 1296. This is sufficient. Statement (2) gives z = 2(3) + y, which depends on y, so it is insufficient.

Multiple choice

Directions: The problem below consists of a question and two statements numbered I and II. Decide whether the data provided in the statements is sufficient to answer the question. Mark the answer as: (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 is required to answer the question What will be the area of the rectangular plot in sq. metres? I. The length of that plot is 5/3 times its breadth. II. The length of a diagonal of that plot is 30 metres.

  1. (1)

  2. (2)

  3. (3)

  4. (4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the area of a rectangle, you need length and breadth. Statement I gives the ratio L = 5/3*B. Statement II gives the diagonal sqrt(L^2 + B^2) = 30. Together, these allow solving for L and B, and thus the area.

Multiple choice

Directions: Each of the question below consists of a question and two statements numbered I and II. Decide whether the data provided in the statements is sufficient to answer the question. Mark answer as: (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 is required to answer the question. What will be the cost of painting the inner walls of a room if the rate of painting is Rs. 20 per sq. m? I. Perimeter of the floor is 44 feet. II. Height of the wall of the room is 12 feet.

  1. (1)

  2. (2)

  3. (3)

  4. (4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the cost of painting the walls, we need the surface area of the four walls, which is (Perimeter of floor) * (Height of wall). Both statements are required to calculate the area.

Multiple choice

Directions: Each of the question below consists of a question and two statements numbered I and II. Decide whether the data provided in the statements is sufficient to answer the question. Mark answer as: (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 is required to answer the question. What will be the value of the second number? I. First number is 60 per cent of the second number. II. 50 per cent of the sum of the first and second numbers is 24.

  1. (1)

  2. (2)

  3. (3)

  4. (4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the numbers be x and y. Statement I gives x = 0.6y. Statement II gives 0.5(x + y) = 24, which simplifies to x + y = 48. Using both equations, we substitute 0.6y for x to get 1.6y = 48, allowing us to solve for y.

Multiple choice

Directions: The problem contains a question and two statements giving certain data. You have to select the correct answer from the given options depending on the sufficiency of the data given in the statements to answer the question. Two cars pass each other in opposite directions. How long would they take to be 500 km apart? (A) The sum of their speeds is 135 kmph. (B) The difference of their speeds is 25 kmph.

  1. Statement (A) by itself is sufficient to answer the question, but statement (B) by itself is not sufficient to answer the question.

  2. Statement (B) by itself is sufficient to answer the question, but statement (A) by itself is not sufficient to answer the question.

  3. Both statements (A) and (B) together are sufficient to answer the question, but neither statement by itself is sufficient to answer the question.

  4. The two statements, even when taken together, are not sufficient to answer the question.

  5. Each statement alone is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the time taken to be 500 km apart, we need the relative speed of the two cars. Statement (A) provides the sum of their speeds, which is the relative speed when moving in opposite directions. Statement (B) provides the difference, which is insufficient without knowing the individual speeds or the sum.