Quantitative Aptitude (CAT)

Algebra Arithmetic Geometry & Mensuration Modern Math Number Systems

Q. A rectangle has an area of 60 square meters and a length of 12 meters. What is the width?

A. 5 meters
B. 6 meters
C. 7 meters
D. 8 meters

Solution

Area = length × width. Thus, 60 = 12 × width, giving width = 60/12 = 5 meters.

Correct Answer: B — 6 meters

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Q. A rectangle's length is 3 times its width. If the area is 75 square meters, what is the length?

A. 15 meters
B. 25 meters
C. 30 meters
D. 20 meters

Solution

Let width = x, then length = 3x. Area = length × width = 3x * x = 3x² = 75. Thus, x² = 25, x = 5, and length = 15 meters.

Correct Answer: A — 15 meters

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Q. A rectangle's length is three times its width. If the perimeter is 64 cm, what is the area of the rectangle?

A. 192 cm²
B. 128 cm²
C. 96 cm²
D. 64 cm²

Solution

Let width = x, then length = 3x. Perimeter = 2(length + width) = 2(3x + x) = 8x = 64, so x = 8 cm. Area = length × width = 3x * x = 3(8)(8) = 192 cm².

Correct Answer: B — 128 cm²

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Q. A rectangular field is 50 meters long and 30 meters wide. If a fence is built around it, what is the total length of the fence?

A. 160 m
B. 140 m
C. 120 m
D. 180 m

Solution

Perimeter = 2(length + width) = 2(50 + 30) = 2 × 80 = 160 m.

Correct Answer: A — 160 m

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Q. A rectangular garden has a length of 12 m and a width of 5 m. If a path of width 1 m is built around it, what is the area of the path?

A. 50 m²
B. 60 m²
C. 70 m²
D. 80 m²

Solution

Area of the garden = 12 × 5 = 60 m². Area of the garden with the path = (12 + 2) × (5 + 2) = 14 × 7 = 98 m². Area of the path = 98 - 60 = 38 m².

Correct Answer: B — 60 m²

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Q. A rectangular garden has a length of 30 meters and a width of 20 meters. What is the area of the garden?

A. 600 m²
B. 500 m²
C. 400 m²
D. 300 m²

Solution

Area = length × width = 30 × 20 = 600 m².

Correct Answer: A — 600 m²

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Q. A rectangular garden is 10 m long and 6 m wide. If a path of width 1 m is built around it, what is the area of the path? (2023)

A. 32 m²
B. 36 m²
C. 40 m²
D. 44 m²

Solution

Area of the garden = 10 * 6 = 60 m². Area including the path = (10 + 2) * (6 + 2) = 12 * 8 = 96 m². Area of the path = 96 - 60 = 36 m².

Correct Answer: B — 36 m²

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Q. A rectangular garden is 30 meters long and 20 meters wide. If a path of 1 meter width is built around it, what is the area of the path?

A. 80 m²
B. 100 m²
C. 120 m²
D. 140 m²

Solution

Area of the garden = 30 × 20 = 600 m². Area including the path = (30 + 2) × (20 + 2) = 32 × 22 = 704 m². Area of the path = 704 - 600 = 104 m².

Correct Answer: B — 100 m²

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Q. A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?

A. 320 m²
B. 400 m²
C. 600 m²
D. 800 m²

Solution

Total area with path = (50 + 4) × (30 + 4) = 54 × 34 = 1836 m². Area of the plot = 50 × 30 = 1500 m². Area of the path = 1836 - 1500 = 336 m².

Correct Answer: B — 400 m²

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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is its volume?

A. 60 cm³
B. 12 cm³
C. 15 cm³
D. 20 cm³

Solution

Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.

Correct Answer: A — 60 cm³

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Q. A rectangular prism has dimensions 3 m, 4 m, and 5 m. What is its surface area?

A. 47 m²
B. 60 m²
C. 70 m²
D. 80 m²

Solution

The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(3*4 + 3*5 + 4*5) = 2(12 + 15 + 20) = 2(47) = 94 m².

Correct Answer: B — 60 m²

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Q. A rectangular prism has dimensions 4 m, 3 m, and 5 m. What is its surface area?

A. 47 m²
B. 60 m²
C. 70 m²
D. 80 m²

Solution

The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*3 + 4*5 + 3*5) = 2(12 + 20 + 15) = 2(47) = 94 m².

Correct Answer: B — 60 m²

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Q. A rectangular prism has dimensions 4 m, 5 m, and 6 m. What is its surface area?

A. 94 m²
B. 60 m²
C. 70 m²
D. 80 m²

Solution

The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*5 + 4*6 + 5*6) = 94 m².

Correct Answer: A — 94 m²

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Q. A retailer bought a bicycle for $300 and sold it for $360. What is the profit percentage?

A. 15%
B. 20%
C. 25%
D. 30%

Solution

Profit = Selling Price - Cost Price = $360 - $300 = $60. Profit Percentage = (Profit / Cost Price) * 100 = ($60 / $300) * 100 = 20%.

Correct Answer: B — 20%

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Q. A retailer bought a watch for $120 and sold it for $150. What is the profit percentage?

A. 20%
B. 25%
C. 30%
D. 15%

Solution

Profit = Selling Price - Cost Price = $150 - $120 = $30. Profit Percentage = (Profit/Cost Price) * 100 = ($30/$120) * 100 = 25%.

Correct Answer: B — 25%

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Q. A retailer buys a bicycle for $300 and sells it for $360. What is the profit percentage? (2023)

A. 15%
B. 20%
C. 25%
D. 30%

Solution

Profit = Selling Price - Cost Price = 360 - 300 = 60. Profit Percentage = (Profit/Cost Price) * 100 = (60/300) * 100 = 20%.

Correct Answer: B — 20%

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Q. A retailer buys a watch for $120 and sells it at a profit of 15%. What is the selling price?

A. $138
B. $140
C. $144
D. $150

Solution

The selling price is calculated as $120 + (15% of $120) = $120 + $18 = $138.

Correct Answer: C — $144

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Q. A retailer buys a watch for $150 and sells it at a profit of 25%. What is the selling price? (2023)

A. $175
B. $180
C. $187.5
D. $200

Solution

Selling Price = Cost Price + Profit = 150 + (25% of 150) = 150 + 37.5 = $187.5.

Correct Answer: C — $187.5

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Q. A retailer buys a watch for $150 and sells it for $180. What is the profit percentage?

A. 15%
B. 20%
C. 25%
D. 30%

Solution

Profit = Selling Price - Cost Price = 180 - 150 = 30. Profit Percentage = (30/150) * 100 = 20%.

Correct Answer: B — 20%

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Q. A retailer buys a watch for $300 and sells it at a profit of 15%. What is the selling price?

A. $345
B. $350
C. $360
D. $375

Solution

Selling Price = Cost Price + Profit = $300 + ($300 * 0.15) = $300 + $45 = $345.

Correct Answer: A — $345

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Q. A retailer sells a bicycle for $300 after applying a discount of 10%. What was the original price of the bicycle?

A. $270
B. $330
C. $300
D. $350

Solution

Let the original price be x. After a 10% discount, the selling price is x - (0.10 * x) = 0.90x. Setting this equal to $300 gives 0.90x = $300, so x = $300 / 0.90 = $333.33.

Correct Answer: B — $330

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Q. A rhombus has diagonals of lengths 12 cm and 16 cm. What is the area of the rhombus?

A. 96 cm²
B. 48 cm²
C. 72 cm²
D. 60 cm²

Solution

Area of a rhombus = (1/2) × d1 × d2. Thus, Area = (1/2) × 12 × 16 = 96 cm².

Correct Answer: A — 96 cm²

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Q. A seller bought a laptop for $800 and sold it at a loss of 10%. What was the selling price?

A. $720
B. $740
C. $760
D. $780

Solution

Selling Price = Cost Price - Loss = 800 - (10% of 800) = 800 - 80 = $720.

Correct Answer: A — $720

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Q. A semicircle has a diameter of 14 cm. What is its area? (Use π ≈ 3.14)

A. 76.96 cm²
B. 48.96 cm²
C. 38.48 cm²
D. 28.96 cm²

Solution

Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².

Correct Answer: A — 76.96 cm²

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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle?

A. 49 cm²
B. 77 cm²
C. 154 cm²
D. 100 cm²

Solution

Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = (1/2) × 3.14 × 49 = 76.96 cm², which rounds to 77 cm².

Correct Answer: B — 77 cm²

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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 3.14)

A. 76.96 cm²
B. 48.96 cm²
C. 38.48 cm²
D. 24.48 cm²

Solution

Area of a semicircle = (1/2) × πr². Radius = 7 cm. Area = (1/2) × 3.14 × (7)² = 76.96 cm².

Correct Answer: A — 76.96 cm²

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Q. A semicircle has a diameter of 14 cm. What is the area of the semicircle? (Use π ≈ 22/7)

A. 77 cm²
B. 49 cm²
C. 154 cm²
D. 88 cm²

Solution

Radius = 7 cm. Area of semicircle = (1/2) × πr² = (1/2) × (22/7) × (7)² = 77 cm².

Correct Answer: A — 77 cm²

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Q. A sequence is defined as 2, 5, 8, 11, ... What is the 15th term of this sequence?

A. 44
B. 41
C. 38
D. 45

Solution

The nth term is given by a + (n-1)d. Here, a = 2, d = 3, and n = 15. So, the 15th term = 2 + (15-1) * 3 = 2 + 42 = 44.

Correct Answer: B — 41

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Q. A sequence is defined as follows: 2, 5, 8, 11, ... What is the 15th term of this sequence?

A. 44
B. 41
C. 38
D. 45

Solution

The first term a = 2 and the common difference d = 3. The 15th term = a + (15-1)d = 2 + 42 = 44.

Correct Answer: B — 41

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Q. A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?

A. 4
B. 5
C. 6
D. 3

Solution

The common difference d can be found using the formula for the nth term. The last term is given by a + (n-1)d. Here, 48 = 12 + (8-1)d, solving gives d = 4.

Correct Answer: A — 4

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Quantitative Aptitude (CAT) MCQ & Objective Questions

Quantitative Aptitude is a crucial component of various competitive exams, including the CAT. Mastering this subject not only enhances your mathematical skills but also boosts your confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps identify important questions and strengthens your grasp of key concepts.

What You Will Practise Here

Number Systems and Properties
Percentage, Profit and Loss
Ratio and Proportion
Time, Speed, and Distance
Averages and Mixtures
Algebraic Expressions and Equations
Data Interpretation and Analysis

Exam Relevance

Quantitative Aptitude is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. In these exams, you can expect questions that test your understanding of basic concepts, application of formulas, and problem-solving skills. Common question patterns include multiple-choice questions that require quick calculations and logical reasoning.

Common Mistakes Students Make

Misunderstanding the question requirements, leading to incorrect answers.
Overlooking units of measurement in word problems.
Not applying the correct formulas for different types of problems.
Rushing through calculations, resulting in simple arithmetic errors.
Failing to interpret data correctly in graphs and tables.

FAQs

Question: What are the best ways to prepare for Quantitative Aptitude in exams?
Answer: Regular practice with MCQs, understanding key concepts, and reviewing mistakes can significantly improve your performance.

Question: How can I improve my speed in solving Quantitative Aptitude questions?
Answer: Practice timed quizzes and focus on shortcuts and tricks to solve problems quickly.

Start solving practice MCQs today to test your understanding of Quantitative Aptitude and enhance your exam readiness. Remember, consistent practice is the key to success!

Quantitative Aptitude (CAT)

Quantitative Aptitude (CAT) MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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