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

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the time taken by Rahul from point P to other point Q ? (I) If he walks 25% faster than his usual speed then he reaches 20 seconds earlier. (II) If he walks 20 km toward point Q from point P at usual speed .after that he takes 10 seconds to reach the point y.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If both statement together are sufficient, but neither statement alone is sufficient.

  5. If statement I and II together are not sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I alone is sufficient. Let usual speed = v and usual time = t. Distance d = v × t. Walking 25% faster means speed = 1.25v, time = t-20. Since distance is constant: v × t = 1.25v × (t-20), which gives t = 100 seconds. Statement II mentions 'point y' which is unclear and doesn't provide enough information to find the time.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer- A student got a total of 430 marks in 5 subjects. How much marks did he get in English? (I) His average marks in other four subjects is 84. (II) His marks in English is 8 more than his average marks in five subjects.

  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. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Other 4 subjects total = 84 × 4 = 336. English = 430 - 336 = 94. Sufficient. Statement II: Average of 5 = 430/5 = 86. English = 86 + 8 = 94. Sufficient. Each statement alone gives the answer.

Multiple choice

The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? A man goes to his office via visiting the passport office and bank. What is the total distance covered by him in the entire journey? I) He covered the distance from his home to the passport office with a speed of 20km/hr, which is 1/3 rd of the total distance between Bank and Office. II)The distance from the passport office to bank and from bank to his office is equal and he covered the distance with a speed of 25km/hr and 30 km/hr respectively in total of 2.5 hrs.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I alone is insufficient because it only gives the relationship between bank-office distance and total distance, but doesn't provide actual distances or times. Statement II alone gives speeds and times for passport-bank and bank-office segments, and states they're equal, but doesn't give the home-passport distance. Together, we can find: Let bank-office = x, so total = 3x. From II: passport-bank = x, time taken for x at 25 km/hr and x at 30 km/hr = 2.5 hrs. x/25 + x/30 = 2.5, which gives x. From I: home-passport = x/3 (since it's 1/3 of bank-office = x). Then total distance = home-passport + passport-bank + bank-office = x/3 + x + x = 7x/3.

Multiple choice

The question given below contains two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer- Find overall profit or loss%? (I) A person purchased 2 bicycle for Rs.1200 each. (II) By selling Ist he gains 20% but on the other he has loss 25%.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together is sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Both statements together are sufficient. Statement I gives purchase price: 2 bicycles at Rs.1200 each = Rs.2400 total. Statement II gives profit/loss percentages: 20% gain on first (profit = Rs.240), 25% loss on second (loss = Rs.300). Net result = Rs.240 - Rs.300 = -Rs.60 (loss). Loss percentage = (60/2400) × 100 = 2.5%. Neither statement alone is sufficient.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the value of x? (I) If 10 is added to x, the result is 34. (II) If x is multiplied by y, the result is 38.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I gives the equation x + 10 = 34, which directly gives x = 24. This alone is sufficient. Statement II gives xy = 38, but without knowing y, we cannot determine x uniquely. Even combining both statements gives y = 38/24 = 19/12, but statement II alone is insufficient. Therefore only statement I alone is sufficient.

Multiple choice

What is the speed of the train? Statement I: The train crosses 150 meters long platform in 45 seconds. Statement II: The train crosses another stationary train of same length in 60 seconds. Statement III: The train crosses a signal pole in 30 seconds.

  1. I and III

  2. I and either II or III

  3. Any two

  4. All three together

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

Statement I alone is insufficient (only platform length and time, no train length). Statement II gives crossing another stationary train of same length in 60 seconds, meaning the train covers twice its length in 60 seconds, so its length L in 30 seconds. Statement III gives crossing a signal pole in 30 seconds (covers L distance). Combining I and III: From III, L = 30×speed. From I: (L+150) = 45×speed. Two equations, two unknowns, so speed can be found. Similarly I and II together are sufficient. Answer: I and either II or III.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: A man can row at a speed of 8 kmph in still water. He goes to a certain upstream point and back to the starting point in a river flowing at 4 kmph. Average speed of man for the total journey. Quantity II: Speed of a cyclist, cycling in a circular ground of radius 7 kilometer, if he takes 4 hour to complete one full round of the ground.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Upstream speed = 8-4 = 4 kmph, Downstream speed = 8+4 = 12 kmph. Average speed for round trip = 2 × product/sum = 2 × 4 × 12 / 16 = 96/16 = 6 kmph. Quantity II: Circumference = 2π × 7 = 14π km. Speed = 14π / 4 = 3.5π ≈ 11 kmph. Since 11 > 6, Quantity II > Quantity I, so Option C is correct.

Multiple choice

Read the following information carefully and decide which information is/are necessary to answer the question. Find the speed of current I. Ratio of upstream speed and downstream speed is 3 : 5. II. Ratio of speed of boat and speed of current is 4 : 1. III. Boat goes to a place 45 km far and come back taking a total time of 5 hours.

  1. All three together are sufficient

  2. Only II is sufficient

  3. Only II and III are sufficient

  4. Only III is sufficient

  5. III and (I or II) are sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find the speed of the current, we need either the ratio of boat speed to current speed (statement II) or information to calculate both speeds. Statement III alone gives distance and total time, but we need the relationship between boat and current speeds to solve. Statement I provides the ratio of upstream:downstream speed (3:5), which combined with III's time data, or combined with II's ratio, is sufficient. Therefore, III with either I or II can solve for current speed.

Multiple choice

What is the speed of the train? I. Train passed a pillar in 18 sec. II. Train passed a platform of equal length in 36 sec. III. The length of train is 300m.

  1. Any two

  2. III and I or II

  3. I and II or III

  4. All three together are sufficient

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

Speed = Distance/Time. From II: Train passes platform of equal length (300m) in 36 seconds, so total distance = 600m. Speed = 600/36. From I+III: Train length = 300m, passes pillar in 18 seconds, so speed = 300/18. Check: 300/18 = 16.67 m/s. 600/36 = 16.67 m/s - consistent. So I+III or II+III gives speed. Option B (III and I or II) is correct. I+II alone doesn't work because we don't know the length.

Multiple choice

Following question consists a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. How many trains arrives at station-B? (I) The ratio of total number of trains arriving at station A and B is 2 : 3. (II) Total 120 trains departs from station B and 80% of the total trains of station-B arrives at station-B.

  1. Only II

  2. Only I

  3. Both from I and II

  4. Any one of the two.

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

Statement I: Ratio of trains at A:B = 2:3, but no absolute numbers. Insufficient alone. Statement II: 120 trains depart from B, and 80% of station-B trains arrive at B. So trains arriving at B = 80% of 120 = 96. Statement II alone is sufficient. However, both together also work and give same answer. The claimed answer C (both) is marked correct, but technically only II is needed.

Multiple choice

The question given below contains two statements numbered I and II giving certain data. You have to decide whether the data given in the statements are sufficient to answer the question. A tank was placed under a shower which was dripping at a uniform rate. At what time was the tank full? Statement 1: The tank was put in place at 2 pm. Statement II: The tank was half full at 3 pm and 75% full at 8 pm on the same day.

  1. if statement I alone is sufficient but statement II alone is not sufficient.

  2. if statement II alone is sufficient but statement I alone is not sufficient.

  3. if either statement I or II is sufficient.

  4. If both statement I and II together are not sufficient.

  5. If both statement I and II together are sufficient, but neither of them alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I only gives the start time (2 pm) but no information about fill rate or initial state. Statement II tells us: 50% filled at 3 pm, 75% at 8 pm. The tank fills 25% in 5 hours, meaning it fills 50% in 10 hours. Since it was 50% full at 3 pm, it will be 100% full at 1 pm the next day. Statement II alone is sufficient.

Multiple choice

Find the length of train A Statement I: Ratio of the speeds of Train A and Train B is 2:3. Statement II: Length of train B is 30% more than that of train A.

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

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

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

  4. If the data even in both the statements I and II together are not sufficient to answer the question.

  5. If the data in both the statements I and II together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find a train's length, we need at least one absolute measurement (actual length or speed with time to cover a distance). Statement I only gives relative speeds, and Statement II only gives relative length. With no anchor values, we cannot determine the actual length of train A.

Multiple choice

Which information are sufficient to answer the questions? What is the speed of the stream? I. The ratio of speed in upstream to the speed in downstream is 2 : 3. II. The distance travelled in upstream in 2 hours by a man is more than distance travelled by him in downstream in 1 hour by 4 km.

  1. I alone

  2. II alone

  3. Any one

  4. Both together are sufficient

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

For stream speed: I gives ratio upstream:downstream = 2:3. If boat=b, stream=s, then (b-s)/(b+s)=2/3, giving b=5s. Not sufficient alone (2 variables, 1 equation). II gives: 2(b-s) = 1(b+s) + 4, giving b-3s=4. Not sufficient alone. Both together: substitute b=5s into b-3s=4, giving 2s=4, s=2 km/h. Both statements together are sufficient.

Multiple choice

Each of given questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. Find track length I. A and B start from X and Y on a track respectively. They move towards each other and meet at 40 meters from X. II. After continuing their journey they made a return and meet at 25 meters from Y. III. Speed of A is 25m/s.

  1. Only I

  2. Only II

  3. I and II together

  4. II and III

  5. None of them are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let track length = L. First meeting at 40m from X means A traveled 40, B traveled (L-40). Second meeting at 25m from Y means A traveled L+25, B traveled 2L-25. From first meeting: distance ratio = speed ratio = 40:(L-40). From second meeting: (L+25):(2L-25) = 40:(L-40). Solving: (L+25)/(2L-25) = 40/(L-40) → (L+25)(L-40) = 40(2L-25) → L² - 15L - 1000 = 80L - 1000 → L² - 95L = 0 → L(L-95) = 0 → L = 95m. So I and II together are sufficient; III (A's speed) is not needed.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: A hovercraft can run 60km/h on still water but due to ocean current its speed is reduced by 20%. And speed on land is 40km/h. find the average speed if its runs same time in ocean and on land? Quantity II: A man drive a car in 4×400m track of a ground. If he completed two and one fourth of round in 5 min 24 sec. Then speed of car is?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Hovercraft speed in still water = 60 km/h. With 20% reduction in ocean: 60 × 0.8 = 48 km/h. Land speed = 40 km/h. When equal time is spent on both, average speed = (48 + 40) / 2 = 44 km/h. Quantity II: Track is 4 × 400m = 1600m per lap. Distance covered = 2.25 × 1600 = 3600m = 3.6 km. Time = 5 min 24 sec = 324 sec = 0.09 hours. Speed = 3.6 / 0.09 = 40 km/h. Since 44 > 40, Quantity I is greater.