Quantitative Aptitude (CAT)

Algebra Arithmetic Geometry & Mensuration Modern Math Number Systems

Q. If x ≡ 4 (mod 7), which of the following could be a possible value of x?

A. 11
B. 10
C. 9
D. 8

Solution

11 mod 7 = 4, so x could be 11.

Correct Answer: A — 11

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Q. In a base 3 system, what is the equivalent of the decimal number 5?

A. 12
B. 21
C. 10
D. 22

Solution

The decimal number 5 is represented as 12 in base 3 (1*3^1 + 2*3^0 = 3 + 2 = 5).

Correct Answer: B — 21

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Q. In a base 3 system, what is the representation of the decimal number 5? (2023)

A. 12
B. 21
C. 10
D. 22

Solution

In base 3, the decimal number 5 is represented as '12' (1*3^1 + 2*3^0 = 3 + 2 = 5).

Correct Answer: B — 21

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Q. In a base 6 number system, what is the decimal equivalent of the number '54'?

A. 30
B. 32
C. 34
D. 36

Solution

'54' in base 6 = 5*6^1 + 4*6^0 = 30 + 4 = 34.

Correct Answer: C — 34

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Q. In a base 6 number system, what is the value of '54'?

A. 30
B. 32
C. 34
D. 36

Solution

'54' in base 6 is calculated as 5*6 + 4 = 30 + 4 = 34 in decimal.

Correct Answer: B — 32

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Q. In a base 6 number system, what is the value of the number 245 in decimal?

A. 73
B. 77
C. 79
D. 81

Solution

To convert from base 6 to decimal, calculate: 2*6^2 + 4*6^1 + 5*6^0 = 2*36 + 4*6 + 5*1 = 72 + 24 + 5 = 101.

Correct Answer: B — 77

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Q. In a base 8 number system, what is the value of the number 57 in decimal?

A. 47
B. 45
C. 49
D. 50

Solution

To convert from base 8 to decimal, calculate: 5*8^1 + 7*8^0 = 5*8 + 7*1 = 40 + 7 = 47.

Correct Answer: A — 47

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Q. In a base 8 system, what is the value of '57'?

A. 45
B. 46
C. 47
D. 48

Solution

'57' in base 8 is calculated as 5*8^1 + 7*8^0 = 40 + 7 = 47.

Correct Answer: B — 46

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Q. In a base-3 number system, what is the product of '10' and '11'?

A. 100
B. 110
C. 101
D. 111

Solution

'10' in base 3 is 3 and '11' is 4. Their product is 12, which is '110' in base 3.

Correct Answer: A — 100

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Q. In a base-3 numeral system, what is the representation of the decimal number 5? (2023)

A. 12
B. 20
C. 21
D. 22

Solution

The decimal number 5 is represented as 21 in base-3 (2*3^1 + 1*3^0 = 5).

Correct Answer: C — 21

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Q. In a base-3 system, what is the decimal equivalent of the number '210'?

A. 6
B. 7
C. 8
D. 9

Solution

'210' in base-3 is 2*3^2 + 1*3^1 + 0*3^0 = 18 + 3 + 0 = 21 in decimal.

Correct Answer: A — 6

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Q. In a base-3 system, what is the sum of the base-3 numbers 12 and 21?

A. 110
B. 100
C. 102
D. 111

Solution

To add in base-3, convert to decimal: 12 (base-3) = 3 + 2 = 5 (decimal) and 21 (base-3) = 2 + 0 = 2 (decimal). The sum is 5 + 2 = 7 (decimal), which is 21 in base-3.

Correct Answer: A — 110

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Q. In a base-4 number system, what is the decimal equivalent of the number '132'?

A. 10
B. 12
C. 14
D. 16

Solution

'132' in base 4 is calculated as 1*4^2 + 3*4^1 + 2*4^0 = 16 + 12 + 2 = 30.

Correct Answer: B — 12

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Q. In a base-4 system, what is the sum of the numbers '12' and '21'?

A. 33
B. 33 in base-4
C. 33 in base-10
D. 30 in base-4

Solution

The sum of '12' and '21' in base-4 is '30' in base-4.

Correct Answer: D — 30 in base-4

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Q. In a base-4 system, what is the sum of the numbers 3 and 2?

A. 11
B. 12
C. 13
D. 20

Solution

In base-4, the sum of 3 and 2 is 11 (3 + 2 = 5 in decimal, which is 11 in base-4).

Correct Answer: A — 11

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Q. In a base-5 number system, what is the decimal equivalent of the base-5 number 243?

A. 35
B. 60
C. 55
D. 50

Solution

To convert from base-5 to decimal, multiply each digit by 5 raised to the power of its position (from right to left, starting at 0). Thus, 2*5^2 + 4*5^1 + 3*5^0 = 2*25 + 4*5 + 3*1 = 50 + 20 + 3 = 73.

Correct Answer: A — 35

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Q. In a base-5 number system, what is the decimal equivalent of the number '243'?

A. 60
B. 61
C. 62
D. 63

Solution

2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

Correct Answer: C — 62

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Q. In a base-5 number system, what is the sum of '23' and '14'?

A. 42
B. 32
C. 41
D. 30

Solution

In base-5, '23' is 2*5 + 3 = 13 and '14' is 1*5 + 4 = 9. Their sum is 22 in decimal, which is '42' in base-5.

Correct Answer: A — 42

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Q. In a base-5 number system, what is the sum of '34' and '21'?

A. 100
B. 110
C. 120
D. 130

Solution

In base-5, '34' is 3*5 + 4 = 19 and '21' is 2*5 + 1 = 11. Their sum is 30, which is '100' in base-5.

Correct Answer: A — 100

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Q. In a base-5 numeral system, what is the decimal equivalent of the base-5 number 243? (2023)

A. 60
B. 50
C. 40
D. 30

Solution

The base-5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60 in decimal.

Correct Answer: A — 60

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Q. In a base-5 numeral system, what is the decimal equivalent of the number 243?

A. 60
B. 61
C. 62
D. 63

Solution

The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

Correct Answer: B — 61

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Q. In a base-5 numeral system, what is the representation of the decimal number 10?

A. 20
B. 22
C. 10
D. 15

Solution

In base-5, the decimal number 10 is represented as 20.

Correct Answer: A — 20

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Q. In a base-5 numeral system, what is the representation of the decimal number 12?

A. 22
B. 23
C. 24
D. 21

Solution

In base-5, the decimal number 12 is represented as 22 (2*5^1 + 2*5^0 = 12).

Correct Answer: B — 23

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Q. In a base-5 numeral system, what is the representation of the decimal number 7?

A. 12
B. 22
C. 14
D. 20

Solution

In base-5, the decimal number 7 is represented as 12, since 1*5^1 + 2*5^0 = 5 + 2 = 7.

Correct Answer: A — 12

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Q. In a base-5 numeral system, which of the following digits is not valid?

A. 0
B. 1
C. 2
D. 5

Solution

In a base-5 numeral system, valid digits are 0, 1, 2, 3, and 4; thus, 5 is not valid.

Correct Answer: D — 5

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Q. In a base-6 number system, what is the product of '12' and '3'?

A. 36
B. 40
C. 42
D. 44

Solution

'12' in base-6 is 1*6 + 2 = 8. '3' is 3. Their product is 8*3 = 24, which is '42' in base-6.

Correct Answer: C — 42

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Q. In a base-6 number system, what is the product of '24' and '13'?

A. 100
B. 110
C. 120
D. 130

Solution

'24' in base-6 is 2*6 + 4 = 16 and '13' is 1*6 + 3 = 9. Their product is 16*9 = 144, which is '100' in base-6.

Correct Answer: A — 100

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Q. In a base-6 number system, what is the product of '5' and '2'?

A. 10
B. 12
C. 14
D. 16

Solution

In base-6, '5' * '2' = 10 in decimal, which is '12' in base-6.

Correct Answer: B — 12

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Q. In a base-7 system, what is the base-10 equivalent of the base-7 number 345?

A. 150
B. 170
C. 180
D. 190

Solution

To convert from base-7 to decimal, calculate 3*7^2 + 4*7^1 + 5*7^0 = 3*49 + 4*7 + 5 = 147 + 28 + 5 = 180.

Correct Answer: B — 170

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Q. In a base-8 number system, what is the product of '7' and '5'?

A. 35
B. 37
C. 40
D. 42

Solution

7*5 = 35 in decimal, which is '43' in base-8.

Correct Answer: C — 40

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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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