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# On the number line

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VP
Joined: 20 Sep 2005
Posts: 1021
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On the number line [#permalink]  03 Apr 2006, 20:26
On the number line <-----------r-------s-----------t--------------->

Is zero halfway between r and s ?

1. s is to the right of zero.
2. The distance b/w t and r is the same as the distance b/w t and -s.
Manager
Joined: 10 Jan 2006
Posts: 116
Followers: 1

Kudos [?]: 2 [0], given: 0

guessing its 'C'

St1 and St 2 together give us

r = -s
hence 0 is halfway between r and s

Senior Manager
Joined: 22 Jun 2005
Posts: 363
Location: London
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Kudos [?]: 5 [0], given: 0

Re: Number line [#permalink]  04 Apr 2006, 02:32
lhotseface wrote:
On the number line <-----------r-------s-----------t--------------->

Is zero halfway between r and s ?

1. s is to the right of zero.
2. The distance b/w t and r is the same as the distance b/w t and -s.

1, t can be to the right or left of zero->Ins
2, r=-s sufficient to answer the question

it's B
Manager
Joined: 13 Dec 2005
Posts: 224
Location: Milwaukee,WI
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Kudos [?]: 7 [0], given: 0

it's B

A --insufficient data
B t-r = t - (-s)
==> r =-s hence 0 is halfway between r and s
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
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1) Not sufficient. r may also be to the right of 0.

2) This doesn't justify that 0 is between r and s.

I can have:

t-r = t+s

r = -s

So 0 must be in between

Ans B
VP
Joined: 20 Sep 2005
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Kudos [?]: 27 [0], given: 0

GMAT Prep says answer is C.
SVP
Joined: 14 Dec 2004
Posts: 1706
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Kudos [?]: 58 [0], given: 0

Me too selected B.

If we consider only statement2; r, s itself can be negative & -s can be positive, it means -s can be on the opposite side of r & s.

<-----------r-------s-----------t------------------ -s >

In this case, we can't say anything.

But statement 1 makes it clear that 0 lies somewhere before 's', hence "C" makes sense.

How does this sound?
Manager
Joined: 30 Jan 2006
Posts: 146
Followers: 1

Kudos [?]: 10 [0], given: 0

Answer B, i.e. stmnt 2 by itself is sufficient.

The stems basically asks is s = -r ? In other words, if zero is exactly between the two, then one is the negative value of the other. Draw a number line to visualize this.

Stmnt 1:
Nothing is said about the property of r. Insufficient.

Stmnt 2:
The distance b/w t and r is the same as the distance b/w t and -s. In other words,

t - r = t - (-s)

t - r = t + s

- r = s

s = -r

Sufficient.
VP
Joined: 20 Sep 2005
Posts: 1021
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Kudos [?]: 27 [0], given: 0

I eliminated this possibility in the test, but I think that was due to test pressure. Your logic looks correct...B gives two possibilites => r,s < 0 or r<0 and s > 0.

vivek123 wrote:
Me too selected B.

If we consider only statement2; r, s itself can be negative & -s can be positive, it means -s can be on the opposite side of r & s.

<-----------r-------s-----------t------------------ -s >

In this case, we can't say anything.

But statement 1 makes it clear that 0 lies somewhere before 's', hence "C" makes sense.

How does this sound?
Manager
Joined: 30 Jan 2006
Posts: 146
Followers: 1

Kudos [?]: 10 [0], given: 0

How can B give two possibilities when stmnt 2 makes it clear that either s is the negative value of r or the other way around?

Confused
VP
Joined: 20 Sep 2005
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Kudos [?]: 27 [0], given: 0

s = -5 => -s = 5,
r = -5 and t = 0.......................One possibility

s =5, r = -5 and t = 10............Second possibility

How can B give two possibilities when stmnt 2 makes it clear that either s is the negative value of r or the other way around?

Confused
Manager
Joined: 20 Feb 2006
Posts: 213
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Kudos [?]: 5 [0], given: 0

I think the answer should be B.
From statement 2,

distance between t and r = distance between t and -s
=> t-r = t+s
=> r+s = 0

Hence, if r+s = 0, answer holds good and we need not worry about the sign of t.

lhotesface,
your first example, r = -5, s = -5 and t = 0
is not correct because it does not satisfy second statement.
VP
Joined: 21 Sep 2003
Posts: 1065
Location: USA
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Kudos [?]: 39 [0], given: 0

lhotseface wrote:
s = -5 => -s = 5,
r = -5 and t = 0.......................One possibility

lhotseface, vivek and others...
s =5, r = -5 and t = 10............Second possibility

What if t =0 and r=5 and s =5... that leads us to E!!

My take on this:
If we are shown 3 numbers on a number line at distinct locations, we should assume that they are not equal and that they have a relationship defined by their corresponding locations. So from the picture I would assume r < s < t

That leaves us with B as the unambiguous answer. Any thoughts?
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

VP
Joined: 20 Sep 2005
Posts: 1021
Followers: 3

Kudos [?]: 27 [0], given: 0

It does since distance b/w t(0) and -s(5) is 5 and the distance b/w t and r is 5 ( distances are always absolute ).

chuckle wrote:
I think the answer should be B.
From statement 2,

distance between t and r = distance between t and -s
=> t-r = t+s
=> r+s = 0

Hence, if r+s = 0, answer holds good and we need not worry about the sign of t.

lhotesface,
your first example, r = -5, s = -5 and t = 0
is not correct because it does not satisfy second statement.
VP
Joined: 20 Sep 2005
Posts: 1021
Followers: 3

Kudos [?]: 27 [0], given: 0

That is what I thought on the test...but the OA is C from GMATPrep. (?!)

In the real exam, I am going to assume such ambiguous questions are experimental, pick a reasonable choice and move on.

giddi77 wrote:
lhotseface wrote:
s = -5 => -s = 5,
r = -5 and t = 0.......................One possibility

lhotseface, vivek and others...
s =5, r = -5 and t = 10............Second possibility

What if t =0 and r=5 and s =5... that leads us to E!!

My take on this:
If we are shown 3 numbers on a number line at distinct locations, we should assume that they are not equal and that they have a relationship defined by their corresponding locations. So from the picture I would assume r < s < t

That leaves us with B as the unambiguous answer. Any thoughts?
VP
Joined: 29 Dec 2005
Posts: 1348
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Kudos [?]: 37 [0], given: 0

giddi77 wrote:
What if t =0 and r=5 and s =5... that leads us to E!!

t cannot be zero since s is right to the zero.

giddi77 wrote:
If we are shown 3 numbers on a number line at distinct locations, we should assume that they are not equal and that they have a relationship defined by their corresponding locations. So from the picture I would assume r < s < t

IMO, in GMAT, unless figures are not supported by the facts, figures are not drawn to scale. therefore, it is possible that the value of r, s and t could be anything.

lhotseface wrote:
On the number line <-----------r-------s-----------t--------------->

Is zero halfway between r and s ?

1. s is to the right of zero.
2. The distance b/w t and r is the same as the distance b/w t and -s.

from i, s is +ve. so not suff.

from ii, if the distance between t and r is the same as the distance between t and -s, then r must equal to s. cuz the distance between any given points is absolute.

so to have the distance between t and s = distance between t and -s, s and r must have the same value. if so then we can say that o is not a halfway between r and s.

so go with B.
Senior Manager
Joined: 24 Jan 2006
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opps i rushed towards the ans. I wrongly read the question

1 helps answering the question but is not sufficient

Intern
Joined: 23 Feb 2006
Posts: 39
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Kudos [?]: 0 [0], given: 0

From 1) We know that t-r=t-(-s) => s=-r But it's possible that s=-r=0 so we can't say whether 0 on a halfwat
From 2) we know that C is NOT zero thus from s=-r we know that r is a not zero negative number while C is not zero positive number
So it's C
VP
Joined: 29 Dec 2005
Posts: 1348
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Kudos [?]: 37 [0], given: 0

Lets see what Honghu and laxi say on this one.
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