CAT 2020Slot 3QAQuestion & Solution
AlgebraMedium
Question
How many pairs(a, b) of positive integers are there such that $a\leq b$ and $ab=4^{2017}$ ?
Options
2018
2019
2017
2020
Solution
$ab\ =\ 4^{2017}=2^{4034}$
The total number of factors = 4035.
out of these 4035 factors, we can choose two numbers a,b such that a
And since the given number is a perfect square we have one set of two equal factors.
.'. many pairs(a, b) of positive integers are there such that $a\leq b$ and $ab=4^{2017}$ = 2018.