If k is not = 0,1, or -1, is 1/k > 0

[acethegmat]

If k is not = 0,1, or -1, is 1/k > 0 ?

1. 1/(k-1) > 0
2. 1/(k+1) > 0

Source Gmat Prep

[geetesht]

Hi, IMO the Ans is 'D' wats the OA?

well this is how i approached this problem:-

I took into consideration that K is not equal to 0,1,-1 before analyzing the statements.

St1) 1/k-1 > 0 only,

Sufficient ,The value of K has to be +ve because if we substitue a -ve value for k the inequality as given is st 1 is not satisfied ! hence 1/k > 0 since K is positive.

st2) 1/k+1 > 0 only,

Sufficient , for all values of k starting for -2,-3,-4 ... onwards the the inequality as given in St2 fails! and the given inequality is satisfied for values of K from 2,3,4... onwards. Hence 1/k is >0

ans: D

the best way to approach such problems is to test numbers!

[mohit_cs2002]

My way of approaching the problem:

Given: K != 0,-1,1
To prove: 1/k>0
i.e. k>0 [to make 1/k +ve, k has to be +ve]

(i) 1/(k-1)>0
i.e. (k-1)>0 [same reasoning as above]
or k>1
which shows that k>0 always. Sufficient

(ii) 1/(k+1)>0
i.e. (k+1)>0 [same reasoning as above]
or k>-1
which shows k can be -0.9 or 2. Since it is not given that k is an integer.Insufficient.

Ans: A

[esledge]

st2) 1/k+1 > 0 only,

Sufficient , for all values of k starting for -2,-3,-4 ... onwards the the inequality as given in St2 fails! and the given inequality is satisfied for values of K from 2,3,4... onwards. Hence 1/k is >0

ans: D

the best way to approach such problems is to test numbers!

I agree that it is often best to test numbers, but I think your work on this one illustrates why it is not always the best way. The biggest danger in picking and testing numbers is "forgetting" to test a value that ends up being critical. Usually people "forget" numbers that don't give the result they seek, or numbers that are just inconvenient (i.e. fractions are less convenient than integers). I put forget in quote here, because it isn't truly forgetting when you don't even think to plug a certain number in the first place.

What you forgot is k = -1/2 (and other numbers like this). Values for k between 0 and -1 agree with statement (2) that 1/(k+1) = 1/positive fraction = positive. Thus, k actually can be negative or positive, as your test numbers showed, and (2) is insufficient.

[geetesht]

st2) 1/k+1 > 0 only,

Sufficient , for all values of k starting for -2,-3,-4 ... onwards the the inequality as given in St2 fails! and the given inequality is satisfied for values of K from 2,3,4... onwards. Hence 1/k is >0

ans: D

the best way to approach such problems is to test numbers!

I agree that it is often best to test numbers, but I think your work on this one illustrates why it is not always the best way. The biggest danger in picking and testing numbers is "forgetting" to test a value that ends up being critical. Usually people "forget" numbers that don't give the result they seek, or numbers that are just inconvenient (i.e. fractions are less convenient than integers). I put forget in quote here, because it isn't truly forgetting when you don't even think to plug a certain number in the first place.

What you forgot is k = -1/2 (and other numbers like this). Values for k between 0 and -1 agree with statement (2) that 1/(k+1) = 1/positive fraction = positive. Thus, k actually can be negative or positive, as your test numbers showed, and (2) is insufficient.

Many thanks Emily . Truly appreciate it !
Hence forth will be a lot more alert while testing numbers...
Could please discuss the algebraic solution to this problem, if there is one!
I've always been comfortable with algebra but some how can't get started on this problem .. :)

[Ben Ku]

Many thanks Emily . Truly appreciate it !
Hence forth will be a lot more alert while testing numbers...
Could please discuss the algebraic solution to this problem, if there is one!
I've always been comfortable with algebra but some how can't get started on this problem .. :)

Since whether 1/k is positive or negative depends on the sign of k, the question is really asking "Is k > 0?"

Statement 1 can be rephrased as k-1 > 0. So that means k > 1. This is sufficient, because if k > 1, then k > 0 as well.

Statement 2 can be rephrased as k+1 > 0. so that meas k > - 1. This is insufficient, because there are values when k > -1 that are negative.

Hope that helps.

[geetesht]

Many thanks Emily . Truly appreciate it !
Hence forth will be a lot more alert while testing numbers...
Could please discuss the algebraic solution to this problem, if there is one!
I've always been comfortable with algebra but some how can't get started on this problem .. :)

Since whether 1/k is positive or negative depends on the sign of k, the question is really asking "Is k > 0?"

Statement 1 can be rephrased as k-1 > 0. So that means k > 1. This is sufficient, because if k > 1, then k > 0 as well.

Statement 2 can be rephrased as k+1 > 0. so that meas k > - 1. This is insufficient, because there are values when k > -1 that are negative.

Hope that helps.

Many Thanks Ben,
there was a good bit of learning involved for me in this sum :)

[Ben Ku]

Glad it helped.