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Data Sufficiency - Intermediate Level: sufficiency analysis INTERMEDIATE

Quick mental agility ★ session: 20 intermediate-level data sufficiency questions. Worksheet 17 of 30 - Focus: sufficiency analysis. Practice information assessment, data completeness, requirement analysis with instant feedback. Great for mid-level students needing moderate complexity with mixed patterns practice.

📝 Worksheet 17 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Data Sufficiency
Worksheet 17 of 30 (56% complete)

Question 1

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 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 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.
geometry, triangles, area

Question 4

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 5

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 6

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 7

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 8

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 9

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 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.
data-interpretation, percentage

Question 11

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 12

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 13

Question: What is the value of x + y? Statement (1): 2x + 3y = 12 Statement (2): 4x + 6y = 24
Statement (2) is just 2 times statement (1). Both represent the same line, infinite solutions. Cannot determine unique x + y.
linear, equations, two-variables

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: Is triangle ABC a right triangle? Statement (1): Sides are 3, 4, and 5 units. Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
geometry, triangles, area

Question 16

Question: Is triangle ABC a right triangle? Statement (1): Sides are 3, 4, and 5 units. Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
geometry, triangles, area

Question 17

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.
geometry, triangles, area

Question 18

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.
linear, equations, two-variables

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 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
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