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CAT 2019 Slot 2 QA Question & Solution

AlgebraMedium

Question

If $5^x - 3^y = 13438$ and $5^{x - 1} + 3^{y + 1} = 9686$, then x + y equals

Solution

$5^x - 3^y = 13438$ and $5^{x - 1} + 3^{y + 1} = 9686$

$5^{x} + 3^{y}*15 = 9686*5$

$5^{x} + 3^{y}*15 = 48430$

16*$3^y$=34992

$3^y$ = 2187

y = 7

$5^x$=13438+2187=15625

x=6

x+y = 13