CAT 2019 Question Paper | Quants Slot 2

CAT Questions

Type in the answer type of questions are generally tricky. They leave you with the anxiousness of whether or not you have come to the right answer as you cannot cross-verify the same with the list of options provided as in other questions. Hence, solving these questions will require a little more attention, a little more focus and a little more practice. The best place to start practicing is the CAT previous year paper questions as they'll set you up for the upcoming CAT exam. Start practicing right away with this beautiful question from CAT 2019 Question Paper Slot 2.

Question 31 : If 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686 , then x+y equals [TITA]

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Video Explanation

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Explanatory Answer

It is given that 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686
Let 5^x-1 = k and 3^y = m
So, 5k - m = 13538 ---- (1)
k + 3m = 9686 ---- (2)
Multiply (1) by 3,
15k - 3m = 40314 ----(3)
Adding (2) and (3) we get,
16k = 50000
k = 625 x 5
k = 5⁵
We know, 5^x-1 = k
So, x - 1 = 5
x = 6

We know, k + 3m = 9686
3125 + 3m = 9686
3m = 6561
m = 2187
m = 3⁷ = 3^y
y = 7

x + y = 6 + 7 = 13

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The question is "If 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686 , then x+y equals [TITA] "

Hence, the answer is 13

 

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