Tag: even and odd numbers

Quizzes (0) Questions (35)

Questions Related to even and odd numbers

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

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

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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

  1. $1001$
  2. $1567$
  3. $2008$
  4. $3003$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. 5/8

  2. 6/7

  3. 7/8

  4. 8/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}=\frac{1}{1+\frac{1}{1+\frac{1}{\frac{2+1}{2}}}}=$
=$\frac{1}{1+\frac{1}{1+\frac{2}{3}}}= \frac{1}{1+\frac{1}{\frac{3+2}{3}}}$
=$\frac{1}{1+\frac{3}{5}}=\frac{1}{\frac{8}{5}}$
=$\frac{5}{8}$
Multiple choice maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

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) $\dfrac{xy}{z} = ab$

  1. Only B

  2. Only C

  3. All the three

  4. Only B and C
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $a+b$
  2. $a+b+1$
  3. $ab$
  4. $ab+2$

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

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?

  1. $1, 2, 3$ and $4$
  2. $1, 2$ and $3$ only
  3. $1$ and $3$ only
  4. $2$ and $4$ only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

Multiplication of one odd and one even integer is always :

  1. Even

  2. Odd

  3. Can't be determined

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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.