ReasoningAbility.com

Data Sufficiency - Beginner Level: sufficient conditions BEGINNER

Master data sufficiency concepts through this speed drill practice set. Worksheet 6 of 30 contains 20 beginner-level problems. Deep dive into sufficient conditions while learning sufficient conditions, data evaluation, information sufficiency. Recommended for entry-level learners aiming for foundational concepts and basic patterns.

📝 Worksheet 6 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 6 of 30 (20% complete)

Question 1

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 2

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 3

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 4

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 5

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 6

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 7

Question: Is triangle ABC equilateral? Statement (1): AB = BC Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
geometry, triangles, area

Question 8

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 9

Question: What is the average weight of the class? Statement (1): Average weight of 20 boys is 60 kg. Statement (2): Average weight of 15 girls is 50 kg.
Combined average = (20×60 + 15×50)/(20+15) = (1200 + 750)/35 = 1950/35 ≈ 55.71 kg.
average, mixture, mean

Question 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

Question: What is the value of x² - y²? Statement (1): x - y = 3 Statement (2): x + y = 7
x² - y² = (x-y)(x+y) = 3 × 7 = 21.
linear, equations, two-variables

Question 19

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 20

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
Previous Worksheet Next Worksheet