CAT 2018 Quant Questions

Question:
If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

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Correct Answer: 54

$f(x + 2) = f(x) + f(x + 1)$

As we can see, the value of a term is the sum of the 2 terms preceding it. 

It has been given that $f(11) = 91$ and $f(15) = 617$.

We have to find the value of $f(10)$.

Let $f(10)$ = b

$f(12)$ = b + 91

$f(13)$ = 91 + b + 91 = 182 + b

$f(14)$ = 182+b+91+b = 273+2b

$f(15)$ = 273+2b+182+b = 455+3b

It has been given that 455+3b = 617

3b = 162

=> b = 54

Therefore, 54 is the correct answer. 

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CAT 2018 Quant Questions
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