Data Sufficiency - Intermediate Level: maximum data INTERMEDIATE

Level up your data sufficiency skills with this comprehensive review. 20 intermediate-level problems await in Worksheet 14 of 30. Focus area: maximum data. Learn data evaluation, information sufficiency, data adequacy through systematic practice. Designed for mid-level learners seeking moderate complexity with mixed patterns.

📝 Worksheet 14 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:

Develop winning strategies for data evaluation
Learn smart approaches to information sufficiency
Optimize your comprehensive review solving technique
Build strategic thinking in data adequacy
Master maximum data through proven methods

Your progress through Data Sufficiency

Worksheet 14 of 30 (46% complete)

Question 1

Question: What is the perimeter of triangle ABC? Statement (1): AB = 5 cm, BC = 7 cm Statement (2): Triangle is isosceles with AC as base

Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.

geometry, triangles, area

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.

speed, distance, time

Question 3

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 4

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 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 (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 6

Question: What is the value of xy? Statement (1): x + y = 7 Statement (2): x² + y² = 25

Using (x+y)² = x² + 2xy + y² → 49 = 25 + 2xy → 2xy = 24 → xy = 12.

linear, equations, two-variables

Question 7

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.

profit, loss, discount

Question 8

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 9

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 10

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 11

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 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 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%.

percentage, profit-loss

Question 14

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 15

Question: How much time will the train take to cover 300 km? Statement (1): The train covers 150 km in 2.5 hours. Statement (2): The train's speed is 60 km/h.

Statement (1): Speed = 60 km/h → time = 300/60 = 5 hours. Statement (2): Directly time = 300/60 = 5 hours.

speed, distance, time

Question 16

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 17

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 18

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.

profit, loss, discount

Question 19

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 20

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

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