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
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Source: Beat The GMAT — Data Sufficiency |
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Talkativetree
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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
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Talkativetree
- Senior | Next Rank: 100 Posts
- Posts: 43
- Joined: Tue Oct 13, 2009 3:31 pm
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
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fruti_yum
- Master | Next Rank: 500 Posts
- Posts: 128
- Joined: Thu Jul 30, 2009 1:46 pm
- Thanked: 1 times
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
