$\frac{Even \times Even}{Even}$

Number Theory Level 2

$\large\frac{a \times b}{c}=d$

for which $a$ , $b$ , $c$ are positive even numbers.

How many of these statements are true?

d can be an even integer
d can be an odd integer
d can be expressed as a fraction, while $c < a \times b$
d can be an irrational number

The answer is 3.

1 solution

Tom Engelsman
Oct 29, 2017

•d can be an even integer (TRUE): take $\frac{(2\alpha)(2\beta)}{2} = 2\alpha\beta$ for $\alpha, \beta \in \mathbb{Z}.$

•d can be an odd integer (TRUE): take $\frac{(6)(10)}{4} = 15.$

•d can be expressed as a fraction, while $c < a \times b$ (TRUE): take $\frac{a \times b}{(3/4)(a \times b)} = \frac{4}{3}.$

•d can be an irrational number (FALSE): $d$ is always rational (i.e. it is always expressible as a fraction with an integral numerator + denominator).

E v e n × E v e n E v e n \frac{Even \times Even}{Even} E v e n E v e n × E v e n ​

The answer is 3.

1 solution

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$\frac{Even \times Even}{Even}$