CAT 2019 Question Paper (Slot 2) Question 79

Question 79

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

Correct Answer: 13

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

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