CAT 2019 Shift 1 Paper

Question : 73 of 100

Marks: +1, -0

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

Your Answer:

Validate

Solution:

Case 1:

m

is even.
Given,

8 f(m+1)-f(m)=2

⇒ 8(m+1+3)-m(m+1)=2

⇒ 8 m+32-m^{2}-m=2

⇒ m^{2}-7 m+30=0

⇒(m-10)(m+3)=0

⇒ m=10 \;\text " or "\;-3

{m}

is positive integer, the only possible value of

{m}=10

.
Case 2:
If

m

is odd, then we would not be getting positive solution.

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