Tag: negative numbers and integers

Questions Related to negative numbers and integers

If the number of consecutive odd integers whose sum can be expressed as $50^2 - 13^2$ is k then k, can be 

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

  1. 33

  2. 35

  3. 37

  4. 39

Show answer
Correct Option: C
Explanation:

Sum of odd $n$ consecutive numbers $n^2$

$\therefore (1+3+5\dots\dots (2n-1))=n^2$
where $n$ represents the number of terms.
$\therefore 50^2=1+3+5\dots 99=50\text{ }terms$
$\therefore 13^2=1+3+5\dots 25=13\text{ }terms$
$\therefore 50^2-13^2$$=(1+3+5\dots 99)-(1+3+5\dots 25)\=(27+29\dots 99)\ =37\text{ }terms.$

The general form of an even number is 

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

  1. $2n-1$

  2. $2n$

  3. $2n+1$

  4. $2$

Show answer
Correct Option: B
Explanation:

An even number is a number which has a factor of $2$.

Therefore, general term will be $2n$

Odd numbers are not divisible by

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

  1. one

  2. two

  3. odd numbers

  4. negative integers

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Correct Option: B
Explanation:

Odd numbers are not divisible by $2$

Difference between two even numbers after and before $2n$, where $n$ is a positive number, is-

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

  1. $0$

  2. $4$

  3. $2$

  4. $6$

Show answer
Correct Option: B
Explanation:
Even number after $2n=2n+2$
Even number before $2n=2n-2$
Difference$=2n+2-\left(2n-2\right)=4$

Pick out even number:
$123, 246, 145, 279$

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

  1. $123$

  2. $ 246$

  3. $ 145$

  4. $279$

Show answer
Correct Option: B
Explanation:

A number is even if the digit in One's place is divisible by $2$.


Out of the numbers $123,246,145,279$ only $246$ is even as it has $6$ at unit's place which is divisible by $2$.

The sum of even numbers between $1$ and $31$ is:

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

  1. $6$

  2. $28$

  3. $240$

  4. $512$

Show answer
Correct Option: C
Explanation:

Let ${S} _{n}=(2+4+6+.....+30)$. This is an A.P in which $a=2,d=2$ and $l=30$
Let the number of terms be $n$. Then,
$a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n=15$
$\therefore$ ${S} _{n}=\cfrac{n}{2}(a+l)=\cfrac{15}{2}\times (2+30)=(15\times 16)=240$.

$-1$ is an odd integer, 5th consecutive integer is

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

  1. Odd

  2. Even

  3. Zero

  4. None

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Correct Option: B
Explanation:

$-5,-4,-3,-2,-1,0,1,2,3,4,5$

This is set of integers in neighbourhood of $-1$ as per number line.
$5$th conescutive integer as seen from above, is $4$ which is Even.

Which one of the following is even?

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

  1. $9 \times 14$

  2. $15 \times 17$

  3. $17 \times 9 $

  4. $11 \times 19$

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Correct Option: A
Explanation:

$9\times 14=9\times 2\times 7$

$\Rightarrow 9\times 14$ has $2$ as one of its factor.
So it is an even number
None of the other options has $2$ as their multiple
So option $A$ is correct.

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. $-2$

Show answer
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. $2m + 1$

Show answer
Correct Option: C
Explanation:

Any even integer is divisible by $2$.

so we can write it as  $2m$