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# On the number line shown, is zero halfway between r and s ?

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Intern
Joined: 09 Feb 2017
Posts: 1
Re: On the number line shown, is zero halfway between r and s ?  [#permalink]

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18 Aug 2017, 23:10
the problem is from statement 2 we get 2 outcomes; s is either positive or r and s are on same point.
from the diagram itself it can be derived that r and s are not on same point that leaves us with only one possibility.
so I will go back to the original query, should we trust the diagram?
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Joined: 11 Nov 2016
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Re: On the number line shown, is zero halfway between r and s ?  [#permalink]

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18 Sep 2017, 00:32
From B:

if r<s<t<0
r = s -----------------------------------(1)

if -s < r < 0 < s < t
r=(-s)----------------------------------(2)

try with a number line, to get a better idea.

In Sufficient.

From A:

s>0 => t> 0 but no details on 'r'

can be 0<r<s<t ---------------------(3)
(OR)
(-s < r < 0 < s < t)-------------------(4)

In Sufficient

From A & B

We have (2) & (4) as common,
=> r= -s
=> 0 is halfway between r & s
Sufficient

Ans: C
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Joined: 08 Apr 2017
Posts: 77
Re: On the number line shown, is zero halfway between r and s ?  [#permalink]

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26 Oct 2017, 17:52
Statement 1 is clearly not enough.

Statement 2: Let's see
Quote:
The distance between t and r is the same as the distance between t and -s

Here only distance is given w.r.t t. Hence this means -s could be equal to r (then 0 is half way between r and s)
or
-s could be to the right of t(r.....0.....t..........-s; here s and r will be on the same side i.e., to the left of 0).

On combining,
we have s as positive so -s has to be to the left of 0 which effectively means -s = r.
Here we have a clear answer that 0 is half way between r and s.

Hence Option C
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Re: On the number line shown, is zero halfway between r and s ?  [#permalink]

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10 Dec 2017, 05:51
This is how i solved through-

Diagram analysis: r<s<t

S1: s is to the right of zero.
In other words, s>0. However, it doesn't say anything about r. Since r<s, r can be anywhere on the number line, as long as it is left of s. So r can be after 0, at 0, or left of 0, so impossible to say if 0 is the midpoint of r and s.

INSUFFICIENT.

S2: The distance between t and r is the same as between t and -s.

Looking at the diagram, if we place -s to the left of s, then for t-r to be equal to t-(-s), r and -s would have to be the same point. -s=r.
In such a case, since 0 is midpoint of s and -s, 0 will be midpoint of s and r.
So answer to the question stem is YES.

But if s and t were on the negative side of the number line, then we have to place -s on the positive side of number line, while r remains on the negative side along with s and t. So still statement 2 condition can be satisfied that distance of t and r equals distance of t and -s. So answer to question stem is NO.

Thus, INSUFFICIENT.

Combining (1) and (2), statement 1 locks the first case we analyzed in statement 2. That is, s and t lie on positive side of number line, therefore -s is on negative side and r has to be the same point as -s. So 0 is midway between r and s, and answer to question is always YES.

Thus, SUFFICIENT.

Posted from my mobile device
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Re: On the number line shown, is zero halfway between r and s ?  [#permalink]

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22 Aug 2018, 21:55
Bunuel Can you please direct me towards more of such 'Number Line' Questions ?
Similar Topics tag is not very helpful in this case!

Thanks !!

DenisSh wrote:

On the number line shown, is zero halfway between r and s?

(1) s is to the right of zero
(2) The distance between t and r is the same as the distance between t and -s

Attachment:
Number line.PNG

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Re: On the number line shown, is zero halfway between r and s ?   [#permalink] 22 Aug 2018, 21:55

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