Mathematics · Quantitative Aptitude

Number Operations and Properties

896 Questions

Improve your quantitative aptitude with these number operations and properties questions. The topics range from basic subtraction and division to highest common factor and roman numerals. Regular practice of these fundamentals builds speed for exams.

Basic arithmetic operationsHCF and number propertiesRoman numeral calculationsNumber series evaluation

Number Operations and Properties Questions

Multiple choice

What is the value of $$M_5$$?

  1. 5

  2. 10

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The value of $$M_5$$ is 15.

Multiple choice

What is the multiplicative identity of a field?

  1. 0

  2. 1

  3. -1

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The multiplicative identity of a field is the element that, when multiplied by any other element of the field, results in that element. In the set of real numbers, the multiplicative identity is 1.

Multiple choice

In the multiplication of two numbers, if one of the numbers is zero, what is the product?

  1. The other number

  2. Zero

  3. The product of the digits of the other number

  4. The sum of the two numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When multiplying two numbers, if one of the numbers is zero, the product is always zero. This is because multiplying any number by zero results in zero.

Multiple choice

What is the value of $S(3, 2)$?

  1. 3

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(3, 2)$ represents the number of ways to partition a set of 3 elements into 2 nonempty subsets. There are 3 ways to do this: {1, 2} and {3}, {1, 3} and {2}, and {2, 3} and {1}. Therefore, $S(3, 2) = 3$.

Multiple choice

What is the value of $S(4, 3)$?

  1. 6

  2. 8

  3. 16

  4. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(4, 3)$ represents the number of ways to partition a set of 4 elements into 3 nonempty subsets. There are 6 ways to do this: {1, 2, 3} and {4}, {1, 2, 4} and {3}, {1, 3, 4} and {2}, {2, 3, 4} and {1}, {1, 2} and {3, 4}, and {1, 3} and {2, 4}. Therefore, $S(4, 3) = 6$.

Multiple choice

What is the value of $S(5, 4)$?

  1. 10

  2. 15

  3. 20

  4. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$S(5, 4)$ represents the number of ways to partition a set of 5 elements into 4 nonempty subsets. There are 15 ways to do this. Therefore, $S(5, 4) = 15$.

Multiple choice

What is the value of $S(6, 5)$?

  1. 20

  2. 30

  3. 40

  4. 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(6, 5)$ represents the number of ways to partition a set of 6 elements into 5 nonempty subsets. There are 20 ways to do this. Therefore, $S(6, 5) = 20$.

Multiple choice

What is the value of $S(7, 6)$?

  1. 35

  2. 45

  3. 55

  4. 65
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(7, 6)$ represents the number of ways to partition a set of 7 elements into 6 nonempty subsets. There are 35 ways to do this. Therefore, $S(7, 6) = 35$.

Multiple choice

What is the value of $S(8, 7)$?

  1. 56

  2. 64

  3. 72

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(8, 7)$ represents the number of ways to partition a set of 8 elements into 7 nonempty subsets. There are 56 ways to do this. Therefore, $S(8, 7) = 56$.

Multiple choice

What is the value of (\binom{5}{2})?

  1. 10

  2. 15

  3. 20

  4. 25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula (\binom{n}{k} = \frac{n!}{k!(n-k)!}), we can calculate (\binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5!}{2!3!} = \frac{120}{2\cdot6} = 10).

Multiple choice

What is 5 + 7?

  1. 12

  2. 14

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To add 5 and 7, you can count on your fingers or use a mental math strategy. Starting with 5, count up 7: 5, 6, 7, 8, 9, 10, 11, 12. Therefore, the answer is 12.

Multiple choice

Subtract 13 from 20.

  1. 7

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To subtract 13 from 20, you can use the counting down method. Starting at 20, count down 13: 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7. Therefore, the answer is 7.

Multiple choice

Find the product of 4 and 9.

  1. 12

  2. 18

  3. 24

  4. 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To multiply 4 and 9, you can use the traditional multiplication algorithm. Multiply 4 by 9, starting from the rightmost digit: 4 x 9 = 36. Therefore, the answer is 36.

Multiple choice

Divide 24 by 6.

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To divide 24 by 6, you can use the division algorithm. Divide 24 by 6, starting from the leftmost digit: 24 ÷ 6 = 4. Therefore, the answer is 4.

Multiple choice

Which number is greater, 12 or 15?

  1. 12

  2. 15

  3. Both are equal
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

15 is greater than 12.