Fractions: Reciprocal
Solve the following non-GMAT question:
>Which of the following is true?
>>I) $$\frac{2}{3}$$ is the reciprocal of 1.5
>>II) 100 is the reciprocal of 0.001
>>III) $$\frac{2}{5}$$ is the reciprocal of $$\frac{3}{5}$$
Correct.
[[snippet]]
I) $$\displaystyle{1.5 = \frac{3}{2}}$$, so $$\displaystyle{\frac{2}{3} \times 1.5 = \left(\frac{2}{3}\right)\left(\frac{3}{2}\right)=1}$$. Hence, 1.5 is the reciprocal of $$\frac{2}{3}$$ and vice versa.
II) $$\displaystyle{100 \times 0.001 = 100 \times \frac{1}{1{,}000} \ne 1}$$. So 0.001 is not the reciprocal of 100.
III) $$\displaystyle{\left(\frac{2}{5}\right)\left(\frac{3}{5}\right) = \frac{6}{25} \ne 1}$$. So $$\frac{2}{5}$$ is not the reciprocal of $$\frac{3}{5}$$.
Incorrect.
[[snippet]]
III) It is true that these fractions **add** to 1, but reciprocals should **multiply** to 1.
> $$\displaystyle{\left(\frac{2}{5}\right)\left(\frac{3}{5}\right) = \frac{6}{25} \ne 1}$$
So $$\frac{2}{5}$$ is not the reciprocal of $$\frac{3}{5}$$.
Incorrect.
[[snippet]]
II) $$\displaystyle{100 \times 0.001 = 100 \times \frac{1}{1{,}000} \ne 1}$$. So 0.001 is not the reciprocal of 100.
Incorrect.
[[snippet]]
II) $$\displaystyle{100 \times 0.001 = 100 \times \frac{1}{1{,}000} \ne 1}$$. So 0.001 is not the reciprocal of 100.
III) It is true that these fractions **add** to 1, but reciprocals should **multiply** to 1.
> $$\displaystyle{\left(\frac{2}{5}\right)\left(\frac{3}{5}\right) = \frac{6}{25} \ne 1}$$
So $$\frac{2}{5}$$ is not the reciprocal of $$\frac{3}{5}$$.
Incorrect.
[[snippet]]
II) $$\displaystyle{100 \times 0.001 = 100 \times \frac{1}{1{,}000} \ne 1}$$. So 0.001 is not the reciprocal of 100.
I only
II only
III only
I and II only
I, II, and III
