Data Interpretation & Data Sufficiency (Class X Level) – Data sufficiency problems
Assam Public Service Commission (APSC)
Combined Competitive Examination (CCE)
Preliminary Examination – General Studies Paper II
(Objective Type, 200 Marks)
Topic: Data Interpretation & Data Sufficiency (Class X Level)
Sub-Topic: Data Sufficiency Problems
📌 Directions (Q1–Q30)
Each question is followed by two statements, Statement (I) and Statement (II).
You have to determine whether the given statements are sufficient to answer the question.
Choose the correct option:
A) Statement (I) alone is sufficient, but Statement (II) alone is not sufficient
B) Statement (II) alone is sufficient, but Statement (I) alone is not sufficient
C) Both Statement (I) and Statement (II) together are sufficient
D) Both Statement (I) and Statement (II) together are not sufficient
MCQs
Q1. What is the value of x?
(I) x + 5 = 15
(II) x − 3 = 7
Answer: A
Explanation:
From (I): x = 10 (sufficient).
From (II): x = 10 (also sufficient).
But (I) alone is enough.
Q2. What is the value of y?
(I) 2y = 14
(II) y + 3 = 10
Answer: A
Explanation:
Statement (I) gives y = 7 directly.
Q3. What is the perimeter of a square?
(I) Length of one side is 6 cm
(II) Area of the square is 36 cm²
Answer: C
Explanation:
(I) gives side = 6 ⇒ perimeter = 24 cm
(II) gives side = √36 = 6 ⇒ perimeter = 24 cm
Both together are sufficient.
Q4. What is the value of x?
(I) 3x − 2 = 10
(II) x² = 16
Answer: A
Explanation:
From (I): x = 4 (unique value).
(II) gives x = ±4 (not sufficient alone).
Q5. What is the average of two numbers?
(I) Their sum is 20
(II) Their difference is 4
Answer: A
Explanation:
Average = sum ÷ 2 = 10.
Statement (I) alone is sufficient.
Q6. What is the value of n?
(I) n is an even number
(II) n = 2k, where k = 5
Answer: B
Explanation:
(I) alone is insufficient.
(II) gives n = 10 (sufficient).
Q7. What is the value of x?
(I) x + y = 10
(II) y = 4
Answer: C
Explanation:
Both together give x = 6.
Q8. What is the speed of a car?
(I) It covers 120 km in 2 hours
(II) Time taken is 2 hours
Answer: A
Explanation:
Speed = distance ÷ time = 120 ÷ 2 = 60 km/h.
(I) alone is sufficient.
Q9. What is the area of a rectangle?
(I) Length = 8 cm
(II) Breadth = 5 cm
Answer: C
Explanation:
Area = length × breadth = 40 cm² (both required).
Q10. What is the value of x?
(I) x² = 25
(II) x > 0
Answer: C
Explanation:
(I) gives x = ±5
(II) restricts x to +5
Both together are sufficient.
Q11. What is the simple interest?
(I) Principal = ₹5,000
(II) Rate = 10% per annum and Time = 2 years
Answer: C
Explanation:
Both statements are required to calculate SI.
Q12. What is the value of y?
(I) 4y = 20
(II) y is a natural number
Answer: A
Explanation:
(I) gives y = 5 directly.
Q13. What is the value of x?
(I) x is a prime number
(II) x < 10
Answer: D
Explanation:
Possible values are multiple (2, 3, 5, 7).
Not sufficient even together.
Q14. What is the value of p?
(I) p : q = 3 : 4
(II) q = 12
Answer: C
Explanation:
From (II), q = 12
Using ratio, p = 9.
Q15. What is the cost of 5 pens?
(I) Cost of 1 pen is ₹10
(II) Total cost is ₹50
Answer: A
Explanation:
Statement (I) alone gives total cost.
Q16. What is the value of x?
(I) 5x = 25
(II) x − 1 = 4
Answer: A
Explanation:
(I) gives x = 5.
Q17. What is the distance travelled?
(I) Speed = 40 km/h
(II) Time = 3 hours
Answer: C
Explanation:
Distance = speed × time = 120 km.
Q18. What is the value of a?
(I) a² = 9
(II) a is negative
Answer: C
Explanation:
(I) gives a = ±3
(II) restricts a = −3.
Q19. What is the total marks obtained?
(I) Average marks = 60
(II) Number of subjects = 5
Answer: C
Explanation:
Total = average × number = 300.
Q20. What is the value of x?
(I) x is an integer
(II) 2x = 8
Answer: B
Explanation:
(II) gives x = 4 directly.
Q21. What is the perimeter of a rectangle?
(I) Length = 10 cm
(II) Breadth = 6 cm
Answer: C
Explanation:
Perimeter = 2(l + b).
Q22. What is the value of y?
(I) y + 5 = 12
(II) y is a whole number
Answer: A
Explanation:
(I) gives y = 7.
Q23. What is the value of n?
(I) n is divisible by 4
(II) n = 2k, where k = 6
Answer: B
Explanation:
(II) gives n = 12.
Q24. What is the average of three numbers?
(I) Their sum is 45
(II) One number is 15
Answer: A
Explanation:
Average = sum ÷ 3 = 15.
Q25. What is the value of x?
(I) x² − 9 = 0
(II) x is positive
Answer: C
Explanation:
x = ±3 from (I), positive condition gives x = 3.
Q26. What is the selling price?
(I) Cost price = ₹200
(II) Profit = 10%
Answer: C
Explanation:
Selling price requires both CP and profit.
Q27. What is the value of y?
(I) 3y + 2 = 11
(II) y < 5
Answer: A
Explanation:
(I) gives y = 3.
Q28. What is the area of a triangle?
(I) Base = 10 cm
(II) Height = 6 cm
Answer: C
Explanation:
Area = ½ × base × height.
Q29. What is the value of x?
(I) x is a multiple of 3
(II) x < 15
Answer: D
Explanation:
Multiple values possible even together.
Q30. What is the value of n?
(I) n + 7 = 20
(II) n is an integer
Answer: A
Explanation:
(I) gives n = 13 directly.
✅ Exam Note
These questions test logical evaluation of statements, a key skill in APSC CCE GS Paper II. Focus on judging sufficiency, not solving fully unless required.
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