Data Sufficiency Worksheet 11 - Beginner-Intermediate Level (statement sufficiency) | 20 Questions

Question 1

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 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 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 5

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 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: 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 8

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.

permutation, combination, counting

Question 9

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.

permutation, combination, counting

Question 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

Question: What is the value of x + y? Statement (1): 2x + 3y = 12 Statement (2): 4x + 6y = 24

Statement (2) is just 2 times statement (1). Both represent the same line, infinite solutions. Cannot determine unique x + y.

linear, equations, two-variables

Question 18

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 19

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 20

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.

permutation, combination, counting

Data Sufficiency - Beginner-Intermediate Level: statement sufficiency BEGINNER-INTERMEDIATE

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20