If the function f(n) is defined as f(n) = n/(n + 1), for all integer

Question

If the function f(n) is defined as f(n) = n/(n + 1), for all integer values of n such that n ≠ –1, which of the following must be true?

I. f(x + 1) > f (x)
II. f(x) > 0
III. f(x) ≠ 0

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only

bluesquare · Accepted Answer

If n = 0, then  f(n)=\frac{n}{n+1}=\frac{0}{1}=0 , which negates II. and III. Therefore the answer has to be A.

GMATinsight · Answer

Checking I. f(x + 1) > f (x)

f(x + 1) =(x+1)/(x+2) and f (x)= (x)/(x+1)

@x=1, f(x+1) = 2/3, f(x) = 1/2 i.e. f(x + 1) > f (x)
@x=2, f(x+1) = 3/4, f(x) = 2/3 i.e. f(x + 1) > f (x)
@x=-3, f(x+1) = 2, f(x) = 3/2 i.e. f(x + 1) > f (x)
@x=-4, f(x+1) = 3/2, f(x) = 4/3 i.e. f(x + 1) > f (x)
@x=-10, f(x+1) = 9/8, f(x) = 10/9 i.e. f(x + 1) > f (x)
@x=-100, f(x+1) = 99/98, f(x) = 100/99 i.e. f(x + 1) > f (x)

CONCEPT: if a/b = c/d where a>b
then, (a+x)/(b+x) < c/d where x > 0

i.e. TRUE

Checking II. f(x) > 0 
Checked with above working already
FALSE

Checking III. f(x) ≠ 0 
@x=0, f(x)=0
i.e. FALSE

Answer: Option  A

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION: Set up a chart to test a representative set of possible x values, including positives, negatives, and zero: 2015-06-15_1214.png I. ALWAYS TRUE: In all cases where f(x) and f(x + 1) were defined, f(x + 1) > f(x). II. USUALLY TRUE: However, f(x) can equal 0 when x = 0. III. USUALLY TRUE: However, f(x) can equal 0 when x = 0. Therefore, only statement I must be true. The correct answer is A.

Alex75PAris · Answer

A faster way:

try some values for f(n)
f(-2) = 2
f(0) = 0
f(1) = 1/2

you see directly that II and III are wrong.
f(x)>0, wrong f(0)=0
f(x) ≠ 0, wrong f(0)=0

So, I only, since you don't have the answer choice "None".

mbaprep2016 · Answer

i have a doubt please correct me where m i wrong
in A

f(x+1) > f(x), so the equation become 
x+1/x+2 > x/x+1
let x =1 
2/3 > 1/2 answer is yes
x= -3
-3+1/-3+2 > -3/-3+1
-2/-1 > -3/-2 i.e. 2> 3/2 yes

what x=-2 solution is not defined, how we deal with this case

bhaskar123 · Answer

Yes , for X=-2 seems a valid number to plug in, this will make f(x+1) undefined . 
(x+1)/(x+2) = (-2+1)/(-2+2) will become undefined. 
But question itself is not bounded by x is not equal to 2, but rather x is not equal to 1.

Can someone please clarify.

TheNightKing · Answer

I solved it fairly quickly so I will mention my approach. The question is asking must be true. So let's try to make it not true. II. f(x) > 0 -- If you try n=-2 you get the value of the function as -2. So this if false III. f(x) ≠ 0 -- Well 0 brings the expression to 0. Now I was actually trying to evaluate options but then I thought do I have an option which says None of these? No? Hence A. 40 seconds

Thank you!

Dj06 · Answer

Solving for A as B and C can easily be eliminated at x=0

lets say f(x+1)=x+1/x+2 and f(x) = x/x+1. Cross multiplying to see if f(x+1) > f(x), we get

LHS = (x+1)(x+1) = x(x+1)+ x+1

RHS = x(x+2) = x(x+1) + x

Hence we see that LHS will also have an extra 1, doesn't matter if x is positive or negative.

PS: please replace x with n.

If the function f(n) is defined as f(n) = n/(n + 1), for all integer

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the function f(n) is defined as f(n) = n/(n + 1), for all integer

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards