Tag: negative numbers and integers

Questions Related to negative numbers and integers

Sum of an even number and an odd number is always an odd number.

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

  1. True

  2. False

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Correct Option: A
Explanation:
$2+3=5$

$16+5=21$

$Even+Odd=Odd$

Hence, it is true.

Multiplicative inverse of $\dfrac{1}{-5}$ is 

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

  1. $\dfrac{1}{-5}$

  2. $-5$

  3. $\dfrac{5}{1}$

  4. $Not\ defined$

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Correct Option: B
Explanation:

As we know that multiplicative inverse of $\cfrac{a}{b}$ will be $\cfrac{b}{a}$.

Therefore,
Multiplicative inverse of $\cfrac{1}{-5} = \cfrac{-5}{1} = -5$

Given that a, b are odd and c, d are even. Then,

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

  1. $\displaystyle a^{2}-b^{2}+c^{2}-d^{2}$ is always divisible by 4

  2. $abc + bcd + cda + dac$ is always divisible by 4

  3. $\displaystyle a^{4}+b^{4}+c^{3}+d^{3}+c^{2}b+a^{2}b$ is always odd

  4. $a + 2b + 3c + 4d$ is odd

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Correct Option: D
Explanation:

Let $a=1, b= 3, c= 2, d = 4$
Option D
$a+2b+3c+4d$
1+6+6+16 =29 which is odd number
In other 3 option always not correct for different values for a, b , c, d

A book has pages numbered 1 to 192 (totally 96 sheets). Some 25 sheets are pulled out of it at random. Then, the sum of these 50 numbers cannot be

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

  1. $1001$

  2. $1567$

  3. $2008$

  4. $3003$

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Correct Option: C
Explanation:

Each of the pulled out $25$ sheets will have an odd number and an even number, back to back.
Therefore, total of numbers on each sheet is odd.
Hence, total of numbers on $25$ sheets is also odd as
when odd number is multiplied to odd number always gives odd number.
Therefore, the total cannot be $2008$, which is even.

The value of $\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+1/2}}}$ on simplification is

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

  1. 5/8

  2. 6/7

  3. 7/8

  4. 8/6

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Correct Option: A
Explanation:
$\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}=\frac{1}{1+\frac{1}{1+\frac{1}{\frac{2+1}{2}}}}=$
=$\frac{1}{1+\frac{1}{1+\frac{2}{3}}}= \frac{1}{1+\frac{1}{\frac{3+2}{3}}}$
=$\frac{1}{1+\frac{3}{5}}=\frac{1}{\frac{8}{5}}$
=$\frac{5}{8}$

Successor of every even number is

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

  1. even

  2. prime

  3. odd

  4. none of these

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Correct Option: C
Explanation:

The successor of an even number is always an odd number. For example, after 26, 27 will come.

So option C is the correct answer.

a, b, c are even numbers and x, y, z are odd numbers. Which of the following relationships can't be justified at any cost?
(a) $\dfrac{a\times b}{c} = x\times y$ (b) $\dfrac{a\times b}{x}=yz$ (c) $\dfrac{xy}{z} = ab$

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

  1. Only B

  2. Only C

  3. All the three

  4. Only B and C

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Correct Option: D
Explanation:

In option B a×b is always even & xyz is always odd therefore equality not holds.

In option C ab is always even therefore abz is also even & xy is always odd hence equality not holds.
In option A xy is always odd but (a×b)/c can be odd or even therefore equality can hold in this case.

If $a$ and $b$ are odd numbers, then which of the following is even?

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

  1. $a+b$

  2. $a+b+1$

  3. $ab$

  4. $ab+2$

  5. None of these

Show answer
Correct Option: A
Explanation:
We know the following rule :

odd + odd = even,

even + even = even,

odd + even = odd,

even + odd = odd,

odd × odd = odd.

(A) The given expression is

a + b = odd + odd = even.

(B) The given expression is

a + b + 1 = odd + odd + odd = even + odd = odd.

(C) The given expression is

ab = odd × odd = odd.

(D) The given expression is

ab + 2 = odd × odd + 2= odd + even = odd.

Thus, the correct option is (A) a+b.

Let S be a set of all even integers. If the operations:
1. addition 2. subtraction 3. multiplication 4. division
are applied to any pair of numbers from S, then for which operations is the resulting number is S?

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

  1. $1, 2, 3$ and $4$

  2. $1, 2$ and $3$ only

  3. $1$ and $3$ only

  4. $2$ and $4$ only

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Correct Option: B
Explanation:

Addition of two even numbers; subtraction of two even numbers and product of two even numbers is an even number.

Multiplication of one odd and one even integer is always :

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

  1. Even

  2. Odd

  3. Can't be determined

  4. None of the above

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Correct Option: A
Explanation:

Even integer is an integer having unit digit as a multiple of $2$

So on multiplication with odd integer, unit digit will still remain a multiple of $2$, hence, multiplication of odd and even integer gives even integer.