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

Ready to master data sufficiency? This benchmark test features 20 beginner-intermediate-level challenges. Worksheet 12 of 30 sharpens your data combination skills. Master requirement analysis, sufficient conditions, data evaluation through guided practice. Perfect for developing test preparation.

📝 Worksheet 12 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 12 of 30 (40% 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: 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.
algebra, equations, basic

Question 4

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 5

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 6

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 7

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 8

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 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).
age, linear-equations

Question 10

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 11

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 12

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 13

Question: What is the diameter of the circle? Statement (1): Area of circle is 154 cm². Statement (2): Circumference is 44 cm.
Statement (1): Area = πr² = 154 → r = 7 cm → diameter = 14 cm. Statement (2): C = πd = 44 → d = 14 cm.
geometry, circles, area

Question 14

Question: What is the value of p? Statement (1): p² = 16 and p > 0 Statement (2): p = 4
Statement (1): p = 4 (positive root). Statement (2): p = 4 directly.
algebra, equations, basic

Question 15

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 16

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 17

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 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 + 7 = 12 Statement (2): 2x = 10
Statement (1): x = 5. Statement (2): x = 5. Both give x = 5 independently.
algebra, equations, basic

Question 20

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
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