Recursive Function Value

CAT 2019 Slot 1 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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.

Answer

Explanation

Let $f(10) = a$ and $f(11) = 91$ . $f(12) = f(10) + f(11) = a + 91$ $f(13) = f(11) + f(12) = 91 + a + 91 = a + 182$ $f(14) = f(12) + f(13) = a + 91 + a + 182 = 2a + 273$ $f(15) = f(13) + f(14) = a + 182 + 2a + 273 = 3a + 455$ Given $f(15) = 617$ : $3a + 455 = 617 \Rightarrow 3a = 162 \Rightarrow a = 54$ .

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Recursive Function Value

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