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Data Sufficiency - Beginner-Intermediate Level: data adequacy BEGINNER-INTERMEDIATE

Strategic fast track practice for data sufficiency: 20 beginner-intermediate-level problems. Worksheet 9 of 30 - Focus: data adequacy. Develop expertise in sufficiency analysis, information assessment, data completeness with step-by-step solutions. Ideal for developing learners targeting building on fundamentals with moderate challenges.

📝 Worksheet 9 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 9 of 30 (30% complete)

Question 1

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 2

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 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 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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 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 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 20

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
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