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Data Sufficiency - Intermediate Level: data necessity INTERMEDIATE

Boost your speed and accuracy with this adaptive style 📈 worksheet. Worksheet 15 of 30 presents 20 intermediate-level data sufficiency problems. Focus on data necessity while practicing data adequacy, sufficiency analysis, information assessment. Difficulty: moderate complexity with mixed patterns. Perfect for mid-level test takers.

📝 Worksheet 15 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 15 of 30 (50% complete)

Question 1

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 2

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 3

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.
inequalities, comparisons

Question 4

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 5

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 6

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 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 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 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 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 11

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 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 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 14

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.
inequalities, comparisons

Question 15

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 16

Question: What is the speed of the train? Statement (1): The train covers 240 km in 4 hours. Statement (2): The train covers 180 km in 3 hours.
Statement (1): Speed = 240/4 = 60 km/h. Statement (2): Speed = 180/3 = 60 km/h.
speed, distance, time

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.
average, mixture, mean

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: 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 20

Question: What is the value of x? Statement (1): x + 7 = 12 Statement (2): 2x = 10
Statement (1): x = 5. Statement (2): x = 5. Both give x = 5 independently.
algebra, equations, basic
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