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Data Sufficiency - Advanced Level: statement sufficiency ADVANCED

Master data sufficiency concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into statement sufficiency while learning requirement analysis, sufficient conditions, data evaluation. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 26 of 30 (86% complete)

Question 1

Question: How much time will the train take to cover 300 km? Statement (1): The train covers 150 km in 2.5 hours. Statement (2): The train's speed is 60 km/h.
Statement (1): Speed = 60 km/h → time = 300/60 = 5 hours. Statement (2): Directly time = 300/60 = 5 hours.
speed, distance, time

Question 2

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.
inequalities, comparisons

Question 3

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.
absolute-value, modulus

Question 4

Question: What is the average of 5 numbers? Statement (1): Sum of the 5 numbers is 250. Statement (2): The numbers are in arithmetic progression with first term 40.
Average = Sum/Count = 250/5 = 50. Statement (1) alone gives answer. Statement (2) alone cannot determine sum without more info.
average, mixture, mean

Question 5

Question: What is the average weight of the class? Statement (1): Average weight of 20 boys is 60 kg. Statement (2): Average weight of 15 girls is 50 kg.
Combined average = (20×60 + 15×50)/(20+15) = (1200 + 750)/35 = 1950/35 ≈ 55.71 kg.
average, mixture, mean

Question 6

Question: How many days will B take to complete the work alone? Statement (1): A and B together complete the work in 12 days. Statement (2): A alone completes the work in 20 days.
1/A + 1/B = 1/12, A = 20 → 1/20 + 1/B = 1/12 → 1/B = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30 → B = 30 days.
work, time, efficiency

Question 7

Question: What is the area of the circle? Statement (1): Circumference is 44 cm. Statement (2): Radius is 7 cm.
Statement (1): C = 2πr = 44 → r = 7 cm → Area = πr² = 154 cm². Statement (2): r = 7 cm directly → Area = 154 cm².
geometry, circles, area

Question 8

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.
absolute-value, modulus

Question 9

Question: What is the cost price of the article? Statement (1): Selling price is Rs. 1200 with a profit of 20%. Statement (2): If sold at Rs. 900, the loss would be 10%.
Statement (1): CP = 1200/1.2 = Rs. 1000. Statement (2): CP = 900/0.9 = Rs. 1000.
profit, loss, discount

Question 10

Question: What is the marked price of the article? Statement (1): After a 10% discount, selling price is Rs. 900. Statement (2): Profit earned is 20% on cost price of Rs. 750.
Statement (1): MP = 900/0.9 = Rs. 1000. Statement (2): SP = 750 × 1.2 = Rs. 900, but discount not given, so MP cannot be determined.
profit, loss, discount

Question 11

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.
inequalities, comparisons

Question 12

Question: What is the total sales of the company across all regions? Statement (1): North region sales are 40% of total, which is Rs. 200,000. Statement (2): South region sales are 25% of total, East region is 20%, West is 15%.
Statement (1): North sales = 40% of total = 200,000 → Total = 200,000/0.4 = Rs. 500,000.
Statement (2): Only percentages given, no absolute values → cannot determine total.
data-interpretation, percentage

Question 13

Question: What is the value of x? Statement (1): x + y = 10 Statement (2): x - y = 4
Adding equations: 2x = 14 → x = 7. Subtracting: 2y = 6 → y = 3. Both statements needed.
linear, equations, two-variables

Question 14

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.
inequalities, comparisons

Question 15

Question: How much time will the train take to cover 300 km? Statement (1): The train covers 150 km in 2.5 hours. Statement (2): The train's speed is 60 km/h.
Statement (1): Speed = 60 km/h → time = 300/60 = 5 hours. Statement (2): Directly time = 300/60 = 5 hours.
speed, distance, time

Question 16

Question: What is the average weight of the class? Statement (1): Average weight of 20 boys is 60 kg. Statement (2): Average weight of 15 girls is 50 kg.
Combined average = (20×60 + 15×50)/(20+15) = (1200 + 750)/35 = 1950/35 ≈ 55.71 kg.
average, mixture, mean

Question 17

Question: How much time will the train take to cover 300 km? Statement (1): The train covers 150 km in 2.5 hours. Statement (2): The train's speed is 60 km/h.
Statement (1): Speed = 60 km/h → time = 300/60 = 5 hours. Statement (2): Directly time = 300/60 = 5 hours.
speed, distance, time

Question 18

Question: What is the total sales of the company across all regions? Statement (1): North region sales are 40% of total, which is Rs. 200,000. Statement (2): South region sales are 25% of total, East region is 20%, West is 15%.
Statement (1): North sales = 40% of total = 200,000 → Total = 200,000/0.4 = Rs. 500,000.
Statement (2): Only percentages given, no absolute values → cannot determine total.
data-interpretation, percentage

Question 19

Question: What is the value of y? Statement (1): y - 5 = 10 Statement (2): y + 3 = 18
Statement (1): y = 15. Statement (2): y = 15. Both give y = 15.
algebra, equations, basic

Question 20

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.
absolute-value, modulus
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