Question 1
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.
Data Sufficiency - Intermediate-Advanced Level: requirement analysis INTERMEDIATE-ADVANCED
Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level data sufficiency questions. Worksheet 20 of 30 hones your requirement analysis abilities. Practice sufficient conditions, data evaluation, information sufficiency under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.
What you'll learn in this worksheet:
- Tackle exam-style sufficient conditions questions with confidence
- Learn time-saving tricks for data evaluation problems
- Practice strategic solving 🎯 techniques for better scores
- Identify and avoid common mistakes in information sufficiency
- Build exam temperament through requirement analysis practice
Your progress through Data Sufficiency
Worksheet 20 of 30 (66% complete)
Question 2
Question: What is the value of x?
Statement (1): x + 7 = 12
Statement (2): 2x = 10
Statement (1): x = 5. Statement (2): x = 5. Both give x = 5 independently.
Question 3
Question: What is the value of x?
Statement (1): x² - 5x + 6 = 0
Statement (2): x is an integer greater than 2
Statement (1): x² - 5x + 6 = 0 → (x-2)(x-3)=0 → x = 2 or 3. NOT sufficient alone (two values).
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Question 4
Question: What is the speed of the train?
Statement (1): The train covers 240 km in 4 hours.
Statement (2): The train covers 180 km in 3 hours.
Statement (1): Speed = 240/4 = 60 km/h. Statement (2): Speed = 180/3 = 60 km/h.
Question 5
Question: What is the value of x?
Statement (1): x² - 5x + 6 = 0
Statement (2): x is an integer greater than 2
Statement (1): x² - 5x + 6 = 0 → (x-2)(x-3)=0 → x = 2 or 3. NOT sufficient alone (two values).
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Question 6
Question: Is x > y?
Statement (1): x² > y²
Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.
Question 7
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.
Question 8
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.
Statement (2): Only percentages given, no absolute values → cannot determine total.
Question 9
Question: What is the cost price of the product?
Statement (1): Selling price is Rs. 1200 and profit is 20%.
Statement (2): If the selling price were 10% higher, the profit would be 32%.
Statement (1): SP = 1200, profit = 20%, so CP = 1200/1.2 = Rs. 1000. SUFFICIENT alone.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Question 10
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.
Question 11
Question: Is integer n divisible by 6?
Statement (1): n is divisible by 2.
Statement (2): n is divisible by 3.
For divisibility by 6, n must be divisible by both 2 and 3. Statement (1) alone: n could be 2,4,6,8,... not all divisible by 6. Statement (2) alone: n could be 3,6,9,12,... not all divisible by 6. Together: n divisible by both 2 and 3 → divisible by LCM(2,3)=6. SUFFICIENT together.
Question 12
Question: What is the value of x?
Statement (1): x² - 5x + 6 = 0
Statement (2): x is an integer greater than 2
Statement (1): x² - 5x + 6 = 0 → (x-2)(x-3)=0 → x = 2 or 3. NOT sufficient alone (two values).
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Statement (2): x > 2 and integer → x could be 3, 4, 5, ... NOT sufficient alone (infinite values).
Together: From (1), x is 2 or 3. From (2), x > 2, so x = 3 uniquely. SUFFICIENT together.
Question 13
Question: What is the cost price of the product?
Statement (1): Selling price is Rs. 1200 and profit is 20%.
Statement (2): If the selling price were 10% higher, the profit would be 32%.
Statement (1): SP = 1200, profit = 20%, so CP = 1200/1.2 = Rs. 1000. SUFFICIENT alone.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Question 14
Question: What is the cost price of the product?
Statement (1): Selling price is Rs. 1200 and profit is 20%.
Statement (2): If the selling price were 10% higher, the profit would be 32%.
Statement (1): SP = 1200, profit = 20%, so CP = 1200/1.2 = Rs. 1000. SUFFICIENT alone.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Statement (2): Let original CP = C, original SP = S.
Profit = (S - C)/C
If SP increases by 10%: new SP = 1.1S, new profit = 32%
(1.1S - C)/C = 0.32
1.1S - C = 0.32C
1.1S = 1.32C
S = 1.2C
This gives ratio S:C = 6:5, but no absolute value. NOT SUFFICIENT alone.
Therefore, only Statement (1) alone is sufficient.
Question 15
Question: In how many ways can the letters of the word be arranged?
Statement (1): The word has 5 distinct letters.
Statement (2): The word has 2 vowels and 3 consonants.
Statement (1): 5 distinct letters can be arranged in 5! = 120 ways.
Statement (2): Without knowing which letters and if any repeats, cannot determine unique arrangements.
Statement (2): Without knowing which letters and if any repeats, cannot determine unique arrangements.
Question 16
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.
Question 17
Question: What is the present age of the father?
Statement (1): The father is 24 years older than his son.
Statement (2): In 6 years, the father will be twice as old as his son.
Let F = father's age, S = son's age.
Statement (1): F = S + 24
Statement (2): F + 6 = 2(S + 6)
Substitute (1) into (2): (S + 24) + 6 = 2S + 12
S + 30 = 2S + 12
18 = S
Then F = 42
Thus, both statements together give unique ages (Father: 42, Son: 18).
Statement (1): F = S + 24
Statement (2): F + 6 = 2(S + 6)
Substitute (1) into (2): (S + 24) + 6 = 2S + 12
S + 30 = 2S + 12
18 = S
Then F = 42
Thus, both statements together give unique ages (Father: 42, Son: 18).
Question 18
Question: What is the value of x?
Statement (1): x + 7 = 12
Statement (2): 2x = 10
Statement (1): x = 5. Statement (2): x = 5. Both give x = 5 independently.
Question 19
Question: Is integer n divisible by 6?
Statement (1): n is divisible by 2.
Statement (2): n is divisible by 3.
For divisibility by 6, n must be divisible by both 2 and 3. Statement (1) alone: n could be 2,4,6,8,... not all divisible by 6. Statement (2) alone: n could be 3,6,9,12,... not all divisible by 6. Together: n divisible by both 2 and 3 → divisible by LCM(2,3)=6. SUFFICIENT together.
Question 20
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.
📈 Building expertise: Worksheet 20 of 30 in Data Sufficiency.