Question 36 Problem Solving 2018 GMAT Quantitative Review

Question 36 Problem Solving 2018 GMAT Quantitative Review

Video explanation [PQID: PS01650]: If r and s are positive integers such that $(2^r)(4^s)=16$…

Comments

SUDHANSHU SINGHsays

the better solution could be splitting 16 into products of 4×4 and rewriting one of the 4 as 2^2 and leaving one 4 as 4^1 and then comparing it to L.H.S would give r=2 and s=1

Yes that is definitely a better way to approach this particular problem. We know both $r$ and $s$ are positive, so they need to be 1 or greater. If $s=1$, then $r=2$, but if $s=2$, then $r=0$, which is not acceptable. And finally $s$ cannot be $3$ or higher for the equation to hold true.

SUDHANSHU SINGH says

the better solution could be splitting 16 into products of 4×4 and rewriting one of the 4 as 2^2 and leaving one 4 as 4^1 and then comparing it to L.H.S would give r=2 and s=1

GMAT Quantum says

Hi Sudhanshu,

Yes that is definitely a better way to approach this particular problem. We know both $r$ and $s$ are positive, so they need to be 1 or greater. If $s=1$, then $r=2$, but if $s=2$, then $r=0$, which is not acceptable. And finally $s$ cannot be $3$ or higher for the equation to hold true.

Thanks,

Dabral