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Data Sufficiency - Expert Level: minimum data EXPERT

Comprehensive self assessment worksheet covering 20 expert-level data sufficiency problems. Worksheet 28 of 30 emphasizes minimum data. Master data evaluation, information sufficiency, data adequacy through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 28 of 30 (93% complete)

Question 1

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 2

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 3

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 4

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 5

Question: What is the value of xy? Statement (1): x + y = 7 Statement (2): x² + y² = 25
Using (x+y)² = x² + 2xy + y² → 49 = 25 + 2xy → 2xy = 24 → xy = 12.
linear, equations, two-variables

Question 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 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 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 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 20

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
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