MBAToronto2024
KarishmaBIs there any shortcut? I used the following technique but failed:
(a+1)/(b+1) > a/b
Exactly what Bunuel did above. With proper fractions, the first point of comparison is 'less than 1/2' or 'more than 1/2'
17/35 and 25/52 are less than 1/2.
9/17, 31/61 and 41/81 are slightly more than 1/2.
In fact, each numerator is 0.5 more.
\(\frac{9}{17} = \frac{8.5}{17} + \frac{0.5}{17}= \frac{1}{2} + \frac{0.5}{17}\)
\(\frac{31}{61} = \frac{30.5}{61} + \frac{0.5}{61} = \frac{1}{2} + \frac{0.5}{61}\)
\(\frac{41}{81} = \frac{40.5}{81} + \frac{0.5}{81}=\frac{1}{2} + \frac{0.5}{81}\)
We can now compare the additional amounts since each has the same numerator of 0.5. Since 9/17 has the smallest denominator, it must be the greatest.
Answer (A)Here is a discussion on another such question: https://youtu.be/6AYRmxkAlrE