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Data Sufficiency - Expert Level: data necessity EXPERT

Intensive progress check 🎯 drill: 20 expert-level data sufficiency questions. Worksheet 30 of 30 hones your data necessity abilities. Practice sufficiency analysis, information assessment, data completeness under timed conditions. Best for expert-level students seeking challenging problems and time-bound practice.

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

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 30 of 30 (100% complete)

Question 1

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.
inequalities, comparisons

Question 2

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

Question 3

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 4

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

Question 5

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 6

Question: How many days will A take to complete the work alone? Statement (1): A and B together complete the work in 6 days. Statement (2): B alone completes the work in 10 days.
Work equation: 1/A + 1/B = 1/6, B = 10 → 1/A = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15 → A = 15 days.
work, time, efficiency

Question 7

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 8

Question: What is the diameter of the circle? Statement (1): Area of circle is 154 cm². Statement (2): Circumference is 44 cm.
Statement (1): Area = πr² = 154 → r = 7 cm → diameter = 14 cm. Statement (2): C = πd = 44 → d = 14 cm.
geometry, circles, area

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.
percentage, profit-loss

Question 10

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 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: How many days will A take to complete the work alone? Statement (1): A and B together complete the work in 6 days. Statement (2): B alone completes the work in 10 days.
Work equation: 1/A + 1/B = 1/6, B = 10 → 1/A = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15 → A = 15 days.
work, time, efficiency

Question 13

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

Question 14

Question: What is the value of x? Statement (1): x + 2y = 8 Statement (2): 2x + 4y = 16
Statement (2) is 2 times statement (1). Both represent same equation. Infinite solutions for x.
linear, equations, two-variables

Question 15

Question: What is the perimeter of triangle ABC? Statement (1): AB = 5 cm, BC = 7 cm Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
geometry, triangles, area

Question 16

Question: What is the value of p? Statement (1): p² = 16 and p > 0 Statement (2): p = 4
Statement (1): p = 4 (positive root). Statement (2): p = 4 directly.
algebra, equations, basic

Question 17

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 18

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 19

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

Question 20

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.
speed, distance, time
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