Consider three integers. In first case the first number is divided by the second number and then the quotient is divided by the third number. In another case the first number is divided by the quotient of the second number and the third number. If the results are same for the cases, then what are the possible values of the third number?

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Solution

The correct options are
A 1
D -1
$Suppose three numbers are a, b and c$ .

$In first case the result is (a \div b) \div c and in the second case the result is a \div (b \div c) .$

According to the question,
$(a \div b) \div c = a \div (b \div c) \frac{\frac{a}{b}}{c} = \frac{a}{\frac{b}{c}} \frac{a}{b c} = \frac{a c}{b} \frac{1}{c} = \frac{c}{1}$
This will only be true if c is either 1 or -1.
Hence, the third number is either +1 or -1.

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