Question

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

• A. Only a
• B. Only c
• C. All the three
• D. Only b and c

Answer 1

The correct option is D Only b and c

Use the rules that

(a) product of two odd or even numbers are odd and even respectively.

(b) the quotient of the odd number $÷$ even number or vice-versa may or may not be strictly odd or even.

a. $ab$ must be a even number and $\frac{ab}{c}$ may be even number or a fraction or odd number and $xy$ must be a odd number
therefore it can be justified in some case.

b. $\frac{ab}{x}$ is always a fraction or even number and $yz$ is always a odd number
therefore it cannot be justified in any case

c.$\frac{xy}{z}$ maybe odd number or fraction but $ab$ will always be even.
therefore it cannot be justified.

Relationships given in b and c can't be justified at any cost.