Data Sufficiency - Beginner Level: sufficiency analysis
BEGINNER
Ready to master data sufficiency? This concept mastery features 20 beginner-level challenges. Worksheet 2 of 30 sharpens your sufficiency analysis skills. Master sufficiency analysis, information assessment, data completeness through guided practice. Perfect for entry-level test preparation.
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Worksheet 2 of 30 (6% 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.
Question 2
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.
Question 3
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).
Question 4
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.
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 (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.
Question 6
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.
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.
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.
Question 9
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.
Question 10
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.
Question 11
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.
Question 12
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.
Question 13
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.
Question 14
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.
Question 15
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.
Question 16
Question: What is the distance between A and B?
Statement (1): A car traveling at 50 km/h takes 3 hours to go from A to B.
Statement (2): A bike traveling at 40 km/h takes 3.75 hours to go from A to B.
Statement (1): Distance = 50 × 3 = 150 km. Statement (2): Distance = 40 × 3.75 = 150 km.
Question 17
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.
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.
Question 19
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.
Question 20
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.