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

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/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

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

ern5231 wrote:Is (1/n) - (1/(n + k)) <1/10?

1. K> 10
2. N> 10

I think the answer is C

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