Tag: negative numbers and integers

Questions Related to negative numbers and integers

If n is an integer, which of the following cannot be odd?

maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

  1. $n+3$

  2. $n+1$

  3. $2n$

  4. $3n$

Show answer
Correct Option: C
Explanation:

We know $2n=2\times n$

So, $2n$ is a multiple of $2$. Hence, it can not be an odd number.
It is always even.

If $|a|$ denotes the absolute value of an integer, then which of the following are correct?
1.$|ab| = |a| |b|$
2. $|a+b| \le |a|+|b|$
3. $|a-b| \ge| |a| -|b||$
Select the correct answer using the code given below.

maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

  1. 1 and 2 only

  2. 2 and 3 only

  3. 1 and 3 only

  4. 1, 2 and 3

Show answer
Correct Option: D
Explanation:

Given $\left| a \right| $ is the absolute value of an integer,

From the definition,
$\left| a \right| =a$ if $ a\ge 0$,
$=-a\quad $ is $a\le0$
$\therefore$ $\left| ab \right| =\left| a \right| \left| b \right| $ where $a,b$ are real numbers.
We know that from the triangle inequality sum of any two sides is always greater than the third side,
i.e.,$\left| a+b \right| \le \left| a \right| +\left| b \right| $,
We can also prove by considering 
Absolute part of the difference between any two sides is always less than the third side,
$\Longrightarrow \left| a-b \right| \ge \left| \left| a \right| -\left| b \right|  \right| $

The difference between a two digit number and the number obtained by interchanged the two digits of the number is $9$. What is the difference between the two digits of number.

maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

  1. $3$

  2. $2$

  3. $1$

  4. Cannot be determined

  5. None of these

Show answer
Correct Option: C
Explanation:
Let the unit's digit be $y$ and ten's digit be $x$.

Then, the number $= 10x + y$. When we interchange the digits, the number will be $10y + x$.

Now, it is given that the difference between a two digit number and the number obtained by interchanged the two digits of the number is $9$, therefore, we have:

$(10x+y)−(10y+x)=9\\ \Rightarrow 9x-9y=9\\ \Rightarrow 9(x-y)=9\\ \Rightarrow x-y=\frac { 9 }{ 9 } \\ \Rightarrow x-y=1$

Hence, the difference between the two digits of number is $1$.

What will come in place of the question mark $(?)$ in the following question?
$34.667-15.597-8.491-0.548=?$

maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

  1. $14.403$

  2. $10.031$

  3. $18.301$

  4. $21.043$

  5. None of these

Show answer
Correct Option: B
Explanation:

Let the missing place in the given question be $x$, then we have:


$34.667-15.597-8.491-0.548=x\ \Rightarrow \dfrac { 34667 }{ 1000 } -\dfrac { 15597 }{ 1000 } -\dfrac { 8491 }{ 1000 } -\dfrac { 548 }{ 1000 } =x\quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow \dfrac { 34667-15597-8491-548 }{ 1000 } =x\ \Rightarrow \dfrac { 34667-(15597+8491+548) }{ 1000 } =x$

$\Rightarrow \dfrac { 34667-24636 }{ 1000 } =x$

$\ \Rightarrow \dfrac { 10031 }{ 1000 } =x\ \Rightarrow x=10.031$

Hence, $34.667-15.597-8.491-0.548=10.031$

Find three consecutive even integers such that the sum of first two integers is same as the sum of third integer and $6$.

maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

  1. $4,6,8$

  2. $6,8,10$

  3. $8,10,12$

  4. $10,12,14$

Show answer
Correct Option: C
Explanation:

Let us say the first even integer be $x$. The second consecutive even integer would be $x+2$ (zit would not be $x+1$ because that would result in an odd integer. The sum of two even integers is even). The third consecutive even integer would be $(x+2)+2$ or $x+4$.


Now, it is given that the sum of first two integers is same as the sum of the third integer and $6$ which means:

$x+(x+2)=(x+4)+6\ \Rightarrow 2x+2=x+10\ \Rightarrow 2x-x=10-2\ \Rightarrow x=8$

Therefore, the first even integer is $8$ then the second integer is $x+2=8+2=10$ and the third integer is $x+4=8+4=12$

Hence, the three consecutive even integers are $8,10,12$.