If n is a positive integer, is 1/n - 1/(n+1)

Question

If n is a positive integer, is  \frac{1}{n} - \frac{1}{n+1} <0.05 ?

(1) n is odd

(2) n is a positive multiple of 7

SheilyKamra · Answer

(1/n)-1/(n+1)<0.05 can also be written as 1/ <0.05 In statement A, consider n as 1 and n+1 as 2; the LHS>RHS; then consider n as 3 and n+1 as 4; still LHS>RHS; then n as 5 and n+1 as 6, LHS

chetan2u · Answer

If n is a positive integer, is \frac{1}{n} - \frac{1}{n+1} <0.05 ? \frac{1}{n} - \frac{1}{n+1} <0.05.............\frac{n+1-n}{n(n+1)}<\frac{5}{100}......n(n+1)>20 We can cross multiply since n is positive, so question is -- Is n(n+1)>20?-- When n is 4.. n(n+1)>20 , thus question becomes is n>4 ? (1) n is odd n can be 3 or 5 or 7.. Insuff (2) n is a positive multiple of 7 n can be 7, 14,..., so n>4 Suff B

lacktutor · Answer

n - a positive integer (\frac{1}{n})-(\frac{1}{n+1}) < 0.05 \frac{(n+1-n)}{n(n+1)} < \frac{1}{20} --> \frac{1}{n(n+1)} < \frac{1}{20} (\frac{1}{20})- \frac{1}{n(n+1)} > 0 \frac{n(n+1)- 20}{n(n+1)*20} >0 \frac{n^{2}+n-20}{n(n+1)*20} >0 \frac{(n+5)(n-4)}{n(n+1)*20} >0 --> n< -5, -14 n is a positive integer --> n>4 ??? (Statement1): n is odd. Clearly insufficient (Statement2): n is a positive multiple of 7 n =7,14,21,.... Sufficient. The answer is B.

fauji · Answer

S1  - n is odd,
take n = 1, we get 0.5 which is equal to RHS(0.5)
take n =3, we get 1/12 which is less than RHS(0.5)
conflicting results -  Insufficient Statement

S2  - n is positive multiple of 7 (7,14,21.....)
take n = 7, we get 1/56 which is less than RHS(0.5)
take n = 14, results less than RHS(0.5)... and so on for higher values. -  Sufficient Statement

Answer is   Option B

Mansi89 · Answer

My question is if 0 is multiple of every number, then n could be 0 too.. please explain where i am wrong.

although I choose B. But this question popped up in my mind.

Posted from my mobile device

lacktutor · Answer

The question says “ if n is positive integer....” —> n > 0(zero). Well, your explanation does not match this solution.

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If n is a positive integer, is 1/n - 1/(n+1) < 0.05?

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