Tag: negative numbers and integers

Quizzes (8) Questions (55)

Questions Related to negative numbers and integers

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

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.

  1. 1 and 2 only

  2. 2 and 3 only

  3. 1 and 3 only

  4. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
D Correct answer
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| $

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

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.

  1. $3$
  2. $2$
  3. $1$

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $1$.
Multiple choice maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

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

  1. $14.403$
  2. $10.031$
  3. $18.301$
  4. $21.043$

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $34.667-15.597-8.491-0.548=10.031$

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

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

  1. $4,6,8$
  2. $6,8,10$
  3. $8,10,12$
  4. $10,12,14$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $8,10,12$.