Tag: operations on integers

Questions Related to operations on integers

Which of the following is positive even integer?

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $4$

  2. $-4$

  3. $0.3$

  4. $-2$

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Correct Option: A
Explanation:

Out of the following the integer which is positive and even is 4. Thus, option A is correct.

Every even integer can be written as  
(Note:  $m$ is any integer)

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $m$

  2. $m + 1$

  3. $2m$

  4. $2m + 1$

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Correct Option: C
Explanation:

Any even integer is divisible by $2$.

so we can write it as  $2m$

If you add two even numbers together, the answer is

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. 0

  2. Always even

  3. Sometimes even

  4. Sometimes odd

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Correct Option: B
Explanation:

If we add two even numbers the answer is always even.

Let $2a$ and $2b$ be two even numbers as both are divisible by $2$
Sum $=2a+2b$
Sum $=2(a+b)$
which is also divisible by $2$ . So the sum is even.
So option $B$ is correct.

If m, n, o, p and q are integers then $m(n + o) (p - q)$ must be even then which of the following is even?

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $m + n$

  2. $n + p$

  3. m

  4. p

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Correct Option: C
Explanation:

$ Given\quad that\quad m,n,o,p\quad and\quad q\quad are\quad integers.\ \therefore \quad (n+o)\quad is\quad an\quad integer\ \quad \quad (p-q)\quad is\quad an\quad integer\ \therefore \quad m(n+o)(p-q)\quad is\quad a\quad product\quad of\quad 3\quad integers.\ The\quad product\quad to\quad be\quad even\quad one\quad of\quad the\quad factors\quad to\quad be\quad even.\ either\quad m\quad be\quad even\longrightarrow option\quad C\ or\quad (n+o)\quad be\quad even\longrightarrow no\quad option\ or\quad (p-q)\quad be\quad even\longrightarrow no\quad option.\ \therefore \quad option\quad C\quad is\quad the\quad answer. $

State whether following statement is true or false. 
Sum of two odd numbers is always an odd number.

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. True

  2. False

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Correct Option: B
Explanation:
$1+3=4\\7+9=16$
Sum of $2$ odd nos. is even

Pick odd ineger:
$3, -4, -3, 5$

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $-4, 5$

  2. $-4,-3$

  3. $3, -3, 5$

  4. $-4$

Show answer
Correct Option: C
Explanation:
An odd number is an integer which is not divisible by two. If it is divided by two, then the result is a fraction. The set of odd integers is $-5,-3,-1,1,3,5,7,.....$

Hence, the odd integers are $3,-3,5$, whereas $-4$ is not an odd integer because it is divisible by $2$.

If you add two odd numbers together, the answer is

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. Always Even

  2. Always Odd

  3. Sometimes Even

  4. 1

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Correct Option: A
Explanation:

If we add two odd numbers the sum is always even.

Let $2n-1$ and $2m-1$ be two odd numbers. 
Sum $=2n-1+2m-1$
Sum $=2n+2m-2$
Sum $=2(n+m-1)$
which is divisible by $2$ . So the sum is even.
Option $A$ is correct.

Write two odd integers lesser than $1$.

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $1,3$

  2. $-1,-3$

  3. $-3,5$

  4. $0,1$

Show answer
Correct Option: B
Explanation:
An odd number is an integer which is not divisible by two. If it is divided by two, then the result is a fraction. The set of odd integers is $-5,-3,-1,1,3,5,7,.....$

The following set of integers is lesser than $1$:

$.....-5,-3,-1,1$

Hence, two of the odd integers lesser than $1$ are $-1,-3$.

If k is a positive integer, then $k(k+1)(k+3)$ is

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. even only when k is even

  2. even only when k is odd

  3. Always odd

  4. Always even

Show answer
Correct Option: D
Explanation:

Suppose $k$ is even

Then $k(k+1)(k+3)$ is even as $k$ will be divisible by $2$
Now if $k$ is odd.
Then $(k+1)$ and $(k+3)$ are even
$\Rightarrow k(k+1)(k+3)$ is also even.
So $k(k+1)(k+3)$ is always even.
So option $D$ is correct.

Write $2$ even integers greater than  $-4$

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $-2,-6$

  2. $-6,-8$

  3. $6,8$

  4. $-3,2$

Show answer
Correct Option: C
Explanation:
An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by $2$, it yields no remainder. The set of even integers is $-6,-4,-2,2,4,6,8,.....$

The following set of integers is greater than $-4$:

$-2,2,4,6,8,.....$

Hence, two of the even integers greater than $-4$ are $6,8$.