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Pls chk if approach is correct?

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Pls chk if approach is correct?

by jimmiejaz » Mon Nov 03, 2008 6:16 am
If n is not equal to 0, is |n| < 4?
1.) n2 > 16
2.)1/|n| > n

My approach:
1.) gives |n| > 4. this gives a def 'no'. so, eliminate b,c,e
2.) gives n|n| < 1
when n>0; n2 < 1 or |n| < 1 which implies 0<n<1 since n > 0
when n<0; -n2 < 1 or |n| > -1 which implies -1<n<0 since n < 0
this is also suff as in both scenarios, |n| < 4.

so ans is D.
Am a bit sceptical in the second. hv i done correctly?

rajiv
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by EricLien9122 » Mon Nov 03, 2008 7:08 am
"when n>0; n2 < 1 or |n| < 1 which implies 0<n<1 since n > 0"

n can be less than 0, the statement just stated n can't equal to 0.

Statement 2 simplifies to 1>n^2 or 1>-n^2

1>n^2:

range of n= -1<n<1, excluding 0.

1>-n^2:

range of n= -1<n<1, excluding 0.


I hope this make sense, please correct me if I made a mistake.
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Re: Pls chk if approach is correct?

by 4meonly » Mon Nov 03, 2008 10:55 am
jimmiejaz wrote: when n<0; -n2 < 1 or |n| > -1 which implies -1<n<0 since n < 0
Not sure but I think here is small mistake
|n| >= 0 always

Agree that (1) is suff

(2)
let n= -1/10 it is |n| < 4
then 1/|n| > n, 10>-1/10

let n= -10 it is |n| > 4
then 1/|n| > n, 1/10>-10
INSUFF

The trap here is that it is not given that n is an integer, it can be a fraction - positive or negative.
In case of -1<n<1 |n| will be less than 4

In case of n<-4 and n>4 |n| will be more than 4
And this will satisfy (2)

Thus, I think A
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Re: Pls chk if approach is correct?

by logitech » Mon Nov 03, 2008 11:15 am
jimmiejaz wrote:If n is not equal to 0, is |n| < 4?
1.) n2 > 16
2.)1/|n| > n

My approach:
1.) gives |n| > 4. this gives a def 'no'. so, eliminate b,c,e
2.) gives n|n| < 1
when n>0; n2 < 1 or |n| < 1 which implies 0<n<1 since n > 0
when n<0; -n2 < 1 or |n| > -1 which implies -1<n<0 since n < 0
this is also suff as in both scenarios, |n| < 4.

so ans is D.
Am a bit sceptical in the second. hv i done correctly?

rajiv
Keep it simple:

The question asks about a distance. Is N less than + 4 or greater than -4

1) Sufficient

n2 > 16 means |n| > 4

2) Sufficient

1/|n| > n

n |n| < 1 :!:

if n = + , then

n^2 < 1 --- > 0 < n < 1

if n = - , then

- n ^ 2 < 1 OR n ^2 > - 1 ----> -1 < n < 0

so n can be between -1 and 1

:idea:

We know the distance is less than 1 unit, which is less than 4 units

IMO, it is D.

What is the OA ?
LGTCH
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by cramya » Mon Nov 03, 2008 6:06 pm
Logitech,
I agree with D)

However I dont with what u said here

n ^ 2 < 1 OR n ^2 > - 1 ----> -1 < n < 0

Lets say n = -10

1/ |n| = 10 > -10 still n < 4 I agree but -10 does not satiisy the

-1 < n < 0

I think if you take the square root of a negative number it will be some i (complex number) out of scope for GMAT

Let me know your thoughts or if I am missing something

My take is either n is neagtive or n is a postive fraction between 0 and 1 for 1/|n| > n
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by cramya » Mon Nov 03, 2008 6:08 pm
Logitech,
I agree with D)

However I dont with what u said here

n ^ 2 < 1 OR n ^2 > - 1 ----> -1 < n < 0

Lets say n = -10

1/ |n| = 1/10 > -10 still n < 4 I agree but -10 does not satiisy the

-1 < n < 0

I think if you take the square root of a negative number it will be some i (complex number) out of scope for GMAT

Let me know your thoughts or if I am missing something

My take is either n is neagtive or n is a postive fraction between 0 and 1 for 1/|n| > n
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by cramya » Mon Nov 03, 2008 6:16 pm
Ok this is my last post for this problem :-) I swear

I think 4MEONLY is right about A)

I contradicted my own example

Let n = -10

1/|n| > n but |n| > 4

Let n = -3 1/|n| > n but |n| < 4

INSUFF


Guys I am done with this one for sure and just wait to hear back from others!!!! Made a meal out of it!!!
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by logitech » Mon Nov 03, 2008 6:29 pm
cramya wrote:Logitech,
I agree with D)

However I dont with what u said here

n ^ 2 < 1 OR n ^2 > - 1 ----> -1 < n < 0

Lets say n = -10

1/ |n| = 1/10 > -10 still n < 4 I agree but -10 does not satiisy the

-1 < n < 0

I think if you take the square root of a negative number it will be some i (complex number) out of scope for GMAT

Let me know your thoughts or if I am missing something

My take is either n is neagtive or n is a postive fraction between 0 and 1 for 1/|n| > n
You are correct my friend.

That's a complex number. "i" and it is out of scope.

But the answer should be still D.

Good catch, thank you very much!
LGTCH
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by cramya » Mon Nov 03, 2008 6:46 pm
Would n=-10 and n=-3 not make statement 2 INSUFF since for n=-10 we get |n| > 4 and for n=-3 we get |n|<4

Inconclusive hence insufficient

Logitech, what r ur thoughts on this?
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by simba12123 » Mon Nov 03, 2008 7:35 pm
According to Cramya and Logitech:
Statement one explains clearly that n is greater than abs. 4
Statement two explains that n is either a positive or negative fraction.

We have an agreement of everyone choosing choice D.

Here is the kink and wet blanket on the party bonfire. Statements 1 and 2 will never disagree on choice D. I am eagerly waiting for a response on this. Great question and applause to all the help!


WHAT IS THE OFFICIAL ANSWER? BOTH LOOK GOOD BUT THEY DONT AGREE
Last edited by simba12123 on Mon Nov 03, 2008 9:34 pm, edited 1 time in total.
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by cramya » Mon Nov 03, 2008 7:59 pm
Simba,
Just to clarify:

I think its A) like 4meonly said and not D) based on n=-10 and n = -3 for stmt II

Hope I am not missing anything! :D
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by 4meonly » Tue Nov 04, 2008 1:35 am
simba12123 wrote: Statements 1 and 2 will never disagree on choice D.
I think this is unwarranted.

Form the idea of DS questions stem 1 and 2 CAN contradict.
What if 1st and 2nd will give you different EXACT answers?
E.g.

bla-bla.What is the value of n?

(1)
bla-bla-bla
You find n=10
SUFF

(2)
bla-bla-bla
You find n=5
SUFF

D
they contradict, but you know exact answer for each stem.

I dont know whether in official GMAT questions stems contradict, but 4me, it is possible.

I still vote for A
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Re: Pls chk if approach is correct?

by jimmiejaz » Tue Nov 04, 2008 2:00 am
jimmiejaz wrote:If n is not equal to 0, is |n| < 4?
1.) n2 > 16
2.)1/|n| > n

My approach:
1.) gives |n| > 4. this gives a def 'no'. so, eliminate b,c,e
2.) gives n|n| < 1
when n>0; n2 < 1 or |n| < 1 which implies 0<n<1 since n > 0
when n<0; -n2 < 1 or |n| > -1 which implies -1<n<0 since n < 0
this is also suff as in both scenarios, |n| < 4.

so ans is D.
Am a bit sceptical in the second. hv i done correctly?

rajiv
Hi all,

I am glad tht so many of you turned up to help. You guys rock!!!!
Sorry, the original answer is A.

Am confused still.
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How crazy!?

by simba12123 » Tue Nov 04, 2008 10:50 am
I was taking an mgmat cat today and saw this question in front of me. LOL I cant really see why D is wrong. Yes we all rock but I need to get a bit more accurate! Can some pros shed some light on this?

Still struggling to see why choice D is insufficient!
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by Stacey Koprince » Tue Nov 04, 2008 2:51 pm
Received a PM asking me to respond. From the top:

Question stem:
n is not zero, so either pos or neg. could be non-integer.
yes/no question
In order for abs. value of n to be < 4, n would have to be between -4 and 4. So I can rephrase:
is -4 < n < 4? (and n is not zero)

(1)
I'll assume "n2" means n^2. Please correct me if that's wrong.
n^2 > 16
n > +4 and n < -4
definitive no. Sufficient. Eliminate B, C, E.

(2)
1/|n| > n
You're testing this as though you have to flip the sign when you multiply things by n, but you don't. n is inside an absolute value sign, and you are multiplying by everything (including the absolute value sign), which means that it's definitely positive (or it could be zero in a different problem, but not in this one, since n does not equal zero).

So you can just say 1 > n * |n| because what you're multiplying by is definitely a positive value. Don't do what a lot of you did next, though, and rewrite this as 1 > n^2. That's not equivalent!

Try some numbers above to understand what that inequality means. If n = -2, then n * |n| = -4. -4 < 1, so this fulfills statement 2. We're allowed to choose n = -2. In this case, n is between -4 and 4, so if n = -2, then the answer to the question is yes.

Now try something else and specifically see whether you can get a "no" answer (since you already have a yes). This requires us to pick something either smaller than -4 or larger than 4. What about n = -10? Then n * |n| = -100 and -100 < 1, so this also fulfills statement 2 and we're allowed to choose n = -10. This time, the answer to the question is no.

Essentially, if we use any negative number at all for n, we'll make the statement true (because if you multiply n by the absolute value of n, you will multiple one negative and one positive number; the result of that is always negative). But some negative numbers will give us a "yes" answer and some will give us a "no" answer.

Insufficient. Answer is A.

(Notice also that the statements do not contradict, as some said above. Statements should never contradict each other.)
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