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Data Sufficiency - Advanced Level: logical sufficiency ADVANCED

Boost your speed and accuracy with this high difficulty set 📈 worksheet. Worksheet 25 of 30 presents 20 advanced-level data sufficiency problems. Focus on logical sufficiency while practicing data completeness, requirement analysis, sufficient conditions. Difficulty: complex scenarios and multi-step problems. Perfect for advanced test takers.

📝 Worksheet 25 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 25 of 30 (83% complete)

Question 1

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 2

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 3

Question: What is the length of chord AB in the circle? Statement (1): Radius of circle is 10 cm. Statement (2): Chord AB subtends 60° at the center.
Chord length = 2r sin(θ/2) = 2 × 10 × sin(30°) = 20 × 0.5 = 10 cm.
geometry, circles, area

Question 4

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 5

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 6

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.
number-theory, divisibility, primes

Question 7

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 8

Question: What is the area of triangle ABC? Statement (1): Base BC = 8 cm Statement (2): Height from A to BC = 5 cm
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm².
geometry, triangles, area

Question 9

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 10

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.
number-theory, divisibility, primes

Question 11

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 12

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 13

Question: What is the distance between A and B? Statement (1): A car traveling at 50 km/h takes 3 hours to go from A to B. Statement (2): A bike traveling at 40 km/h takes 3.75 hours to go from A to B.
Statement (1): Distance = 50 × 3 = 150 km. Statement (2): Distance = 40 × 3.75 = 150 km.
speed, distance, time

Question 14

Question: Is integer n a prime number? Statement (1): n > 10 Statement (2): n < 20 and n is odd
Statement (1): n > 10 could be prime (11,13,17,19) or composite (12,14,15,16,18) - NOT sufficient. Statement (2): n is odd between 10 and 20: possibilities are 11,13,15,17,19. Among these, 15 is composite - NOT sufficient. Together: Same as statement (2) alone - still ambiguous (15 is composite, others prime). NOT sufficient even together.
number-theory, divisibility, primes

Question 15

Question: Is integer n a prime number? Statement (1): n > 10 Statement (2): n < 20 and n is odd
Statement (1): n > 10 could be prime (11,13,17,19) or composite (12,14,15,16,18) - NOT sufficient. Statement (2): n is odd between 10 and 20: possibilities are 11,13,15,17,19. Among these, 15 is composite - NOT sufficient. Together: Same as statement (2) alone - still ambiguous (15 is composite, others prime). NOT sufficient even together.
number-theory, divisibility, primes

Question 16

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.
percentage, profit-loss

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).
age, linear-equations

Question 18

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 19

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 20

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.
quadratic, algebra
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