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Is 1/a < 1/(b+1)? 1. a=b 2. b>0

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Is 1/a < 1/(b+1)? 1. a=b 2. b>0 [#permalink]

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New post 17 Nov 2008, 16:57
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Is 1/a < 1/(b+1)?
1. a=b
2. b>0

Pls explain your answer.

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 17 Nov 2008, 17:05
Not sure if someone has an elegant solution to it - i'd be interested in seeing one. But for test taking purposes, here's how I would tackle the problem.

Looking at the first data:
Knowing that a=b does not provide sufficient information. When b is negative, then 1/a > 1/(b+1) whereas when b is positive then 1/a < 1/(b+1)

Looking at the second data:
Knowing b>0 alone does not provide sufficient information. a could be any number so 1/a could be greater or less than 1/(b+1).

Looking at the two data combined:
If a is equal to b and b is a positive number (thus a is a positive number) then we have sufficient information to answer to question. if we sub in a for b, the question becomes is 1/a < 1/(a+1) where a is positive? The answer is intuitively no.

Thus, 1 and 2 combined is enough to answer the question but neither alone is sufficient.

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 17 Nov 2008, 17:06
1/a < 1/(b+1) <=> 1/a - 1/(b+1) < 0

<=> (b+1-a)/[a(b+1] < 0

(1) a = b
Q <=> 1/[a(a+1]<0
<=> a(a+1) < 0 ==> insuff

if -1<a<0 => 1/a < 1/(b+1)
if a not in (-1,0) => 1/a > 1/(b+1)

(2) b > 0 insuff

(1) & (2)

a = b > 0 => 1/a > 1/(b+1) suff
Answer C

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 17 Nov 2008, 22:12
C.
(1) doesnt tell us a is +ve or -ve.
(2) insuff.

from (1) and (2), a>0 so the inequality is indeed false.

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 17 Nov 2008, 22:54
sfwon wrote:
Not sure if someone has an elegant solution to it - i'd be interested in seeing one. But for test taking purposes, here's how I would tackle the problem.

Looking at the first data:
Knowing that a=b does not provide sufficient information. When b is negative, then 1/a > 1/(b+1) whereas when b is positive then 1/a < 1/(b+1)

Looking at the second data:
Knowing b>0 alone does not provide sufficient information. a could be any number so 1/a could be greater or less than 1/(b+1).

Looking at the two data combined:
If a is equal to b and b is a positive number (thus a is a positive number) then we have sufficient information to answer to question. if we sub in a for b, the question becomes is 1/a < 1/(a+1) where a is positive? The answer is intuitively no.

Thus, 1 and 2 combined is enough to answer the question but neither alone is sufficient.


For data 1), when a=b and b is positive, lets just take a=b=4, then 1/4 > 1/5, correct? So when a=b>0, I think 1/a > 1/(b+1) (not 1/a < 1/(b+1) as you pointed out).
So my conclusion is with a=b, we can always conclude that 1/a > 1/(b+1) - thus the answer should be A as data 1 is sufficient to answer the question.
Where did I go wrong here?

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 18 Nov 2008, 08:24
(1) doest say b>0..so a=b could be 0.
nganle08 wrote:
sfwon wrote:
Not sure if someone has an elegant solution to it - i'd be interested in seeing one. But for test taking purposes, here's how I would tackle the problem.

Looking at the first data:
Knowing that a=b does not provide sufficient information. When b is negative, then 1/a > 1/(b+1) whereas when b is positive then 1/a < 1/(b+1)

Looking at the second data:
Knowing b>0 alone does not provide sufficient information. a could be any number so 1/a could be greater or less than 1/(b+1).

Looking at the two data combined:
If a is equal to b and b is a positive number (thus a is a positive number) then we have sufficient information to answer to question. if we sub in a for b, the question becomes is 1/a < 1/(a+1) where a is positive? The answer is intuitively no.

Thus, 1 and 2 combined is enough to answer the question but neither alone is sufficient.


For data 1), when a=b and b is positive, lets just take a=b=4, then 1/4 > 1/5, correct? So when a=b>0, I think 1/a > 1/(b+1) (not 1/a < 1/(b+1) as you pointed out).
So my conclusion is with a=b, we can always conclude that 1/a > 1/(b+1) - thus the answer should be A as data 1 is sufficient to answer the question.
Where did I go wrong here?

Kudos [?]: 58 [0], given: 0

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Re: DS - is 1/a < 1/(b+1) [#permalink]

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New post 18 Nov 2008, 09:24
Thanks, everyone.
OA is C.

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Re: DS - is 1/a < 1/(b+1)   [#permalink] 18 Nov 2008, 09:24
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