Question

State T for True and F for False.
i) If an even number is divided by 2, the quotient is always odd.
ii) All even numbers are composites numbers.
iii) The LCM of two co-prime numbers cannot be equal to their product.
iv) Every number is a factor of itself
For (i) (ii) (iii) (iv)
A) T T F F
B) F F F T
C) T F T T
D) F F T T

Answer 1

Hint: This question can be solved based on divisibility of numbers, factor of the number, composites numbers and Least common multiple of two numbers. When a number (dividend) is divided by another number (divisor) then the answer is quotient. Composites numbers are those who have more than two factors. Each number has at least two factors 1 and number itself. The LCM i.e. least common multiple is the smallest common number which is a multiple of both the numbers. And a factor is the number which divides into another number exactly and without leaving a remainder.

Complete step-by-step solution:
Let us check one by one statement.
i) If an even number is divided by 2, the quotient is always odd.
When a number (dividend) is divided by another number (divisor) then the answer is quotient. So if we divide an even number by 2, the quotient may be even or odd. Like if we divide even number 22 by 2 then \[\dfrac{{22}}{2} = 11\], so quotient is odd number but if we divide even number 20 by 2 then \[\dfrac{{20}}{2} = 10\] quotient is even number. So if an even number is divided by 2, then the quotient may be odd or even. So the statement is a false statement.
ii) All even numbers are composites numbers.
Composites numbers are those who have more than two factors. Each number has at least two factors 1 and number itself. All even numbers have more than two factors except number 2. Number 2 has only two factors that are 1 and 2. So number 2 is not a composite number but it is a prime number. So the statement all even numbers are composite numbers is a false statement.
iii) The LCM of two co-prime numbers cannot be equal to their product.
The LCM i.e. least common multiple is the smallest common number which is a multiple of both the numbers. Two co-prime numbers have no common factor between them. So the LCM of the two co-prime numbers is always their product. So the statement that LCM of two co-prime numbers cannot be equal to their product is a wrong statement.
iv) Every number is a factor of itself.
Every number has at least two factors 1 and number itself. So every number is a factor of itself. So the statement is true.
Considering T for true statement and F for false statement, we can say F F F T for above four statements.

So the Option (B) is the correct answer.

Note: Co-prime numbers have 1 as a common factor while if two prime numbers have difference of 2 is called twin prime numbers. E.g. 3 and 5, 59 and 61, 71 and 73. Two prime numbers will always coprime but one prime and another composite numbers may not be coprime to each other.