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 what is the value of m?

Answer Choices

Correct answer marked below

1

3

4

6

10

Correct

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

KasturikaJun 23

I got m=3 but not sure if that's right. Let me check my work: if m=3 (odd), f(m)=6, f(m+1)=f(4)=20, so 2*20-6=34 not 2. So something's off.

RolandsJun 30

Wait, I think you mixed up the function definition. Check the problem again.

HiteshJun 30

I did the same at first! The formula is 8f(m+1)-f(m)=2, not 2f(m+1)-f(m).

RishabhSep 18

This was tricky because you have to test both parity cases for m. I liked it though, good practice for function problems.

SwarupSep 25

Yeah, definitely a 700-level trap. I initially forgot to consider m even vs odd.

ElliottAug 10

Can someone explain why m=4 doesn't work? I plugged it in and got 8f(5)-f(4)=8*8-20=44, not 2. So it's not that.

CallanAug 18

Because if m=4 is even, then f(m)=m(m+1)=4*5=20, and m+1=5 odd so f(5)=5+3=8. 8*8-20=44. So yeah, not 2.

SamruddhiMay 21

Nice question. I solved it by setting up equations for both parities. For m odd: f(m)=m+3, m+1 even so f(m+1)=(m+1)(m+2). Then 8(m+1)(m+2)-(m+3)=2. That simplifies to 8m^2+23m+11=0, which gives no positive integer. For m even: f(m)=m(m+1), m+1 odd so f(m+1)=m+4. Then 8(m+4)-m(m+1)=2 => 8m+32-m^2-m=2 => m^2-7m-30=0 => (m-10)(m+3)=0, so m=10. Answer E. Took me a while but got there.

MohitaJun 3

Thanks for the detailed breakdown! I missed the simplification initially.

What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

For any positive integer n, let f(n)=n(n+1)f(n)=n(n+1)f(n)=n(n+1) if n is even, and f(n)=n+3f(n)=n+3f(n)=n+3 if n is odd. If m is a positive integer such that 8f(m+1)−f(m)=28f(m+1)-f(m)=28f(m+1)−f(m)=2, then what is the value of m?