Data Sufficiency Questions for Competitive Exams

Data Sufficiency Questions for Competitive Exams

Data Sufficiency in Data Interpretation

Introduction

Data Sufficiency is an important topic under Data Interpretation (DI) and Quantitative Aptitude sections of competitive exams like SSC, Banking (IBPS, SBI), CAT, MAT, Railways, and other government exams. These questions test a candidate’s logical thinking and decision-making ability, not lengthy calculations.

What is Data Sufficiency?

In Data Sufficiency, candidates are given:

  • A question
  • Followed by two or more statements

The task is not to solve the question completely, but to decide whether the given statements are sufficient to answer the question.

Objective of Data Sufficiency Questions

The main aim is to check:

  • Analytical ability
  • Understanding of mathematical concepts
  • Ability to identify relevant vs irrelevant data
  • Logical reasoning skills

Speed and accuracy play a crucial role here.

Standard Answer Choices in Data Sufficiency

Most exams follow a fixed pattern of answer options:

  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 Statement I and Statement II together are sufficient
  4. Both statements together are not sufficient
  5. Either Statement I or Statement II alone is sufficient

Understanding these options is key to solving questions quickly.

Types of Data Sufficiency Questions in Data Interpretation

1. Arithmetic-Based Data Sufficiency

Questions based on:

  • Percentage
  • Profit & Loss
  • Ratio & Proportion
  • Simple & Compound Interest

2. Table or Chart-Based Data Sufficiency

Statements may include:

  • Bar graphs
  • Pie charts
  • Line graphs
  • Tabular data

Candidates must check whether the data provided is enough to answer the question.

3. Logical Data Sufficiency

Focuses on:

  • Conditions
  • Comparisons
  • Logical relationships

Example of a Data Sufficiency Question

Question:
What is the average marks scored by a student in 5 subjects?

Statement I:
The total marks scored by the student is 400.

Statement II:
The student scored equal marks in all subjects.

Analysis:

  • Statement I alone is sufficient (Average = Total ÷ Number of subjects)
  • Statement II alone is not sufficient

✅ Correct Answer: Statement I alone is sufficient

Data Sufficiency Questions

1. What is the average of five numbers?

I. The sum of the five numbers is 250.
II. The highest number among them is 60.

2. What is the percentage increase in salary?

I. The old salary was ₹20,000.
II. The new salary is ₹25,000.

3. What is the total number of students in a class?

I. The ratio of boys to girls is 3:2.
II. There are 18 boys in the class.

4. What is the profit earned on selling an article?

I. The cost price of the article is ₹800.
II. The selling price of the article is ₹1,000.

5. What is the value of x?

I. 2x + 5 = 15
II. x − 3 = 2

6. What is the total expenditure of a company in a year?

I. The company spent 40% of its income on salaries.
II. The total income of the company is ₹50 lakh.

7. What is the ratio of apples to oranges?

I. There are 40 apples.
II. There are 60 fruits in total.

8. What is the speed of a train?

I. The train covers 300 km in 5 hours.
II. The train stops for 30 minutes during the journey.

9. What is the simple interest earned?

I. Principal is ₹10,000 and rate is 10% per annum.
II. Time period is 2 years.

10. What is the total number of employees in an office?

I. 60% of employees are male.
II. The number of female employees is 80.

11. What is the average marks scored by a student?

I. The student scored 360 marks in 6 subjects.
II. The maximum marks in each subject is 100.

12. What is the distance between two cities?

I. A car travels at 60 km/h for 4 hours.
II. The car takes a break of 30 minutes.

13. What is the total sales of a shop in a month?

I. Sales in the first 15 days were ₹2 lakh.
II. Sales in the next 15 days were ₹3 lakh.

14. What is the value of y?

I. 3y = 27
II. y² = 81

15. What is the average age of a group of people?

I. Total age of the group is 300 years.
II. There are 10 people in the group.

16. What is the total profit of a company?

I. Total revenue is ₹10 crore.
II. Total expenditure is ₹7 crore.

17. What is the percentage of students who passed an exam?

I. 120 students passed the exam.
II. Total number of students appeared is 200.

18. What is the cost price of an article?

I. Selling price is ₹1,200.
II. Profit percentage is 20%.

19. What is the average rainfall in a year?

I. Total rainfall over 12 months is 1,200 mm.
II. Rainfall was uniform throughout the year.

20. What is the total number of books sold by a publisher?

I. 30% of books were sold online.
II. 70% of books were sold offline and the number is 7,000.

21. What is the value of a pie chart sector?

I. The sector represents 25% of the total.
II. The total value represented is 360 units.

22. What is the average speed of a journey?

I. Distance covered is 240 km.
II. Total time taken is 6 hours.

23. What is the total production of a factory?

I. The factory produces 500 units per day.
II. The factory works for 20 days in a month.

24. What is the number of students who failed?

I. Total students are 500.
II. 80% students passed the exam.

25. What is the value of the missing data in a table?

I. The total of all entries is 1,000.
II. The sum of known entries is 750.

Answer

1. Average of five numbers

  • I: Sum = 250 ⇒ Average = 250 ÷ 5 = 50 ✅
  • II: Highest number alone cannot give average ❌
    Answer: A

2. Percentage increase in salary

  • Need old + new salary.
  • I alone = old salary only ❌
  • II alone = new salary only ❌
  • Both together → Percentage Increase = ((New − Old)/Old) × 100 ✅
    Answer: C

3. Total students in class

  • I alone: ratio 3:2 ⇒ cannot know total ❌
  • II alone: 18 boys ⇒ cannot know total ❌
  • Both together: Boys = 18, ratio 3:2 ⇒ total students = 30 ✅
    Answer: C

4. Profit earned

  • Profit = Selling Price − Cost Price
  • I alone: Only cost price ❌
  • II alone: Only selling price ❌
  • Both together → Profit = 1000 − 800 = 200 ✅
    Answer: C

5. Value of x

  • I: 2x + 5 = 15 → x = 5 ✅
  • II: x − 3 = 2 → x = 5 ✅
  • Either statement alone sufficient ✅
    Answer: E

6. Total expenditure

  • I: 40% of income on salaries ❌ (Income unknown)
  • II: Total income = ₹50 lakh ❌ (Expenditure breakdown unknown)
  • Both together → Expenditure = 50% × 40% = ₹20 lakh ✅
    Answer: C

7. Ratio of apples to oranges

  • I: 40 apples alone ❌
  • II: 60 fruits alone ❌
  • Both together: Oranges = 60 − 40 = 20 ⇒ Ratio = 40:20 = 2:1 ✅
    Answer: C

8. Speed of train

  • I: Distance = 300 km, Time = 5 h ⇒ Speed = 60 km/h ✅
  • II alone: Stop time only ❌
    Answer: A

9. Simple Interest

  • SI = (P × R × T)/100
  • I: P and R known ❌
  • II: T known ❌
  • Both together → SI = 10000 × 10 × 2 /100 = 2000 ✅
    Answer: C

10. Total employees

  • I: 60% male ❌ (Total unknown)
  • II: Female = 80 ❌ (Male unknown)
  • Both together → Total = 80 / 0.4 = 200 ✅
    Answer: C

11. Average marks

  • I: Total marks = 360, Subjects = 6 (from question)
  • Average = 360 ÷ 6 = 60 ✅
  • II alone: Maximum marks irrelevant ❌
    Answer: A

12. Distance between two cities

  • I: Speed × Time = 60 × 4 = 240 km ✅
  • II alone: Stop time only ❌
    Answer: A

13. Total sales

  • I: 2 lakh, II: 3 lakh
  • Both together → Total = 2 + 3 = 5 lakh ✅
    Answer: C

14. Value of y

  • I: 3y = 27 → y = 9 ✅
  • II: y² = 81 → y = ±9 ❌ (not unique)
    Answer: A

15. Average age

  • I: Total age = 300 ❌ (Number of people unknown)
  • II: Number of people = 10 ❌ (Total unknown)
  • Both together → Average = 300 / 10 = 30 ✅
    Answer: C

16. Total profit

  • Profit = Revenue − Expenditure = 10 − 7 = 3 crore ✅
  • Both statements needed ✅
    Answer: C

17. Percentage of students passed

  • % Passed = (120/200) × 100 = 60 ✅
  • Both statements needed ✅
    Answer: C

18. Cost price of article

  • Profit % = 20%, SP = 1200
  • CP = SP / (1 + Profit%) = 1200 / 1.2 = 1000 ✅
  • Both statements needed ✅
    Answer: C

19. Average rainfall

  • I: Total = 1200 mm → Average = 1200 / 12 = 100 mm ✅
  • II alone: Rainfall uniform → average unknown without total ❌
    Answer: A

20. Total books sold

  • I: 30% sold online ❌ (total unknown)
  • II: 70% = 7000 → Total = 7000 / 0.7 = 10,000 ✅
    Answer: B

21. Pie chart sector value

  • I: 25% alone ❌ (Need total value)
  • II: Total value = 360 ❌ (Need % of sector)
  • Both together → Sector = 25% of 360 = 90 ✅
    Answer: C

22. Average speed

  • Average speed = Distance ÷ Time = 240 ÷ 6 = 40 km/h ✅
  • Both statements together needed ✅
    Answer: C

23. Total production

  • Total = Daily × Number of days = 500 × 20 = 10,000 ✅
  • Both statements needed ✅
    Answer: C

24. Students who failed

  • Total − Passed = 500 − (80% of 500 = 400) = 100 ✅
  • Both statements needed ✅
    Answer: C

25. Missing data in table

Both statements needed ✅
Answer: C

Total − Known = 1000 − 750 = 250 ✅