Data Sufficiency - Beginner-Intermediate Level: logical sufficiency
BEGINNER-INTERMEDIATE
Intensive quick response training 🎯 drill: 20 beginner-intermediate-level data sufficiency questions. Worksheet 10 of 30 hones your logical sufficiency abilities. Practice information assessment, data completeness, requirement analysis under timed conditions. Best for developing students seeking building on fundamentals with moderate challenges.
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Worksheet 10 of 30 (33% complete)
Question 1
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.
Question 2
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 3
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.
Question 4
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.
Question 5
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 6
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 7
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 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: 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 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.
Question 11
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 12
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 13
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 14
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.
Question 15
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 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.
Question 17
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.
Question 18
Question: What is the value of y?
Statement (1): y - 5 = 10
Statement (2): y + 3 = 18
Statement (1): y = 15. Statement (2): y = 15. Both give y = 15.
Question 19
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 20
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.