i think the answer is B.
choices A&D can be ruled out because the first statement doesn't tell you anything about the value of N which is essentially what you need to compare the answer too.
So you're left with BCE. B must be sufficient because when you substitute 10 for N you see that you have 1/10 - (1/(10+k)). So no matter what that denominator comes out to be... you're still subtracting something from the 1/10 which will result in a number less than 1/10.
I hope that's correct
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
213 less or more
Source: Beat The GMAT — Data Sufficiency |
Is (1/n) - (1/(n + k)) <1/10?
1. K> 10
2. N> 10
Answer is C imo.
(1) insufficient because no idea what N is.
(2) insufficient alone because k can be negative. if k=-12, N=11, then
1/11 - 1/(11-12)< 1/10
1/11-(1/(-1)< 1/10
1/11-(-1)< 1/10
1/11+1 < 1/10
12/11 is not < 1/10
TOGETHER, we know that
1/(>10) - 1/[(>10)+(>10)] < 1/10
which at bare minimum (K=N=10.000001, which rounds to 10) means basically
1/10 - 1/20 < 1/10
1/20 < 2/20
1. K> 10
2. N> 10
Answer is C imo.
(1) insufficient because no idea what N is.
(2) insufficient alone because k can be negative. if k=-12, N=11, then
1/11 - 1/(11-12)< 1/10
1/11-(1/(-1)< 1/10
1/11-(-1)< 1/10
1/11+1 < 1/10
12/11 is not < 1/10
TOGETHER, we know that
1/(>10) - 1/[(>10)+(>10)] < 1/10
which at bare minimum (K=N=10.000001, which rounds to 10) means basically
1/10 - 1/20 < 1/10
1/20 < 2/20
(1/n) - (1/(n + k)) <1/10
(n + k - n)/((n + k)n) < 1/10
10k < n(n + k) ?
This is what its asking now
i> says K > 10
thus,
100 < n (n + k) ?
if n > 16...this is wrong, however, if n< = 16, this is true
so we can't say anything...Not sufficient
ii> says n > 10
10k < 10 ( 10 + k)
k < 10+ k ??
ohh yes we can say for sure that its always true..So sufficient
Answer should be B...
Please provide OA...thanks
(n + k - n)/((n + k)n) < 1/10
10k < n(n + k) ?
This is what its asking now
i> says K > 10
thus,
100 < n (n + k) ?
if n > 16...this is wrong, however, if n< = 16, this is true
so we can't say anything...Not sufficient
ii> says n > 10
10k < 10 ( 10 + k)
k < 10+ k ??
ohh yes we can say for sure that its always true..So sufficient
Answer should be B...
Please provide OA...thanks
you mistake is that you're multiplying and dividing by variables that may or may not be negatives when you're in an inequality problem.
lets say we have
(n + k - n)/((n + k)n) < 1/10
k/[n(n+k)] < 1/10
look at my solution
2. N> 10
if n=100, but k = -101, then
k/[n(n+k)] < 1/10
-101/[100(100-101)} < 1/10
-101/-100 < 1/10
basically 1 < 1/10, which is false
lets say we have
(n + k - n)/((n + k)n) < 1/10
k/[n(n+k)] < 1/10
look at my solution
2. N> 10
if n=100, but k = -101, then
k/[n(n+k)] < 1/10
-101/[100(100-101)} < 1/10
-101/-100 < 1/10
basically 1 < 1/10, which is false
I think the answer is Cern5231 wrote:Is (1/n) - (1/(n + k)) <1/10?
1. K> 10
2. N> 10
we arrive at equation k/n(n+k) < 0.1
therefore we need both values of n and k to arrive at a definite answer..
if k is 11.. and n = 11.. we ge the vlaue of 0.04 which is less than 0.1..
any value higher than 11 for either of the two variables will give a value less than 0.04.. therefore, less than 0.1
We can say definitively that value is less than 0.1
hence C
