On the number line : Quant Question Archive [LOCKED]
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# On the number line

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VP
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03 Apr 2006, 20:26
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
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03 Apr 2006, 20:37
guessing its 'C'

St1 and St 2 together give us

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

Senior Manager
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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
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04 Apr 2006, 02:42
it's B

A --insufficient data
B t-r = t - (-s)
==> r =-s hence 0 is halfway between r and s
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04 Apr 2006, 05:27
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
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04 Apr 2006, 08:38
GMAT Prep says answer is C.
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04 Apr 2006, 08:49
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
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04 Apr 2006, 08:51
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
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04 Apr 2006, 08:54
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
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04 Apr 2006, 08:57
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
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04 Apr 2006, 09:09
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
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04 Apr 2006, 12:29
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.
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04 Apr 2006, 12:34
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?
_________________

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- Bernard Edmonds

VP
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04 Apr 2006, 16:42
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
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04 Apr 2006, 16:46
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
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04 Apr 2006, 17:29
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.
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04 Apr 2006, 19:04
opps i rushed towards the ans. I wrongly read the question

1 helps answering the question but is not sufficient

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05 Apr 2006, 06:16
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
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05 Apr 2006, 11:10
Lets see what Honghu and laxi say on this one.
05 Apr 2006, 11:10
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