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# If s and t are two different numbers on the number line, is

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Director
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If s and t are two different numbers on the number line, is [#permalink]

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27 Apr 2010, 10:04
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If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t
[Reveal] Spoiler: OA

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11 May 2010, 03:56
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harikattamudi wrote:
37.If 'S' and 'T' are two different numbers on the number liine, is S + T equal to 0?
(1) The distance between S and 0 is the same as the distance between T and 0.
(2) 0 is between S and T

What does the tern between in the stmt. 2 Mean .. Does that mean exactly in the middle or some where between S and T. Please explain What does between mean in terms of GMAT.

Thanks
-H

0 is between s and t, means 0 is somewhere between s and t on the number line.

If GMAT wants to tell that 0 is exactly between s and t, it would usually state that as "0 is halfway between s and t on the number line", which always can be expressed as $$\frac{s+t}{2}=0$$.

TIPS:
On the GMAT we can often see such statement: $$z$$ is halfway between $$x$$ and $$y$$ on the number line. Remember this statement can ALWAYS be expressed as:

$$\frac{x+y}{2}=z$$.

"The distance between x and y" can always be expressed as $$|x-y|$$.

Hope it helps.
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Director
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27 Apr 2010, 10:16
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mbafall2011 wrote:
LM wrote:

C?

S and T can be on the same side of zero, ie s==t.

Knowing zero lies between s and t doesnt help as it may not be in the center. knowing both, we call tell one is negative and the other is equally positive

S == t is not possible because it is given that they are different numbers. So think again........

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27 Apr 2010, 10:51
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LM wrote:

If s and t are two different numbers on the number line, is s + t = 0 ?

Note: "the distance between x and y on the number line equals to z" always can be expressed as $$|x-y|=z$$.

Given $$s\neq{t}$$. Q: $$s+t=0$$? OR is $$s=-t$$

(1) Distance between s and 0 is the same as distance between t and 0 --> $$|s-0|=|t-0|$$ --> $$|s|=|t|$$. As $$s\neq{t}$$, then $$s=-t$$. Sufficient.

(2) 0 is between s and t --> 0 is somewhere between s and t on the number line. Not sufficient.

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Re: If s and t are two different numbers on the number line, is [#permalink]

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11 May 2013, 03:46
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rajathpanta wrote:
I read between as middle. Isnt the word between confusing???

You mean you read "between" as "middle" in "distance between t and 0"? What does it means then?
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Re: If s and t are two different numbers on the number line, is [#permalink]

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17 Dec 2015, 10:47
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Key observations:

1. It is a number line. SO don't draw the xy plane.
2. The numbers are "DIFFERENT".

Reframing the question: Is S = -T.

Statement 1 is sufficient to give the answer.

Statement 2 is insufficient. Between does not mean between and in the middle of. Earth is between Jupiter and Sun. Does not mean midway.
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27 Apr 2010, 10:09
LM wrote:

C?

S and T can be on the same side of zero, ie s==t.

Knowing zero lies between s and t doesnt help as it may not be in the center. knowing both, we call tell one is negative and the other is equally positive

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27 Apr 2010, 10:40
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Because S and T are two different numbers from Stem.

From (1), distance between S and 0 is the same as 0 and T on the number line, that implies S=-T or T=-S and hence S+T=0 -- Sufficient

From (2), 0 is in between S and T. It doesn't say anything about the distance ... hence S+T is not necessarily 0. -- Not Sufficient.

A.

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10 May 2010, 17:41
37.If 'S' and 'T' are two different numbers on the number liine, is S + T equal to 0?
(1) The distance between S and 0 is the same as the distance between T and 0.
(2) 0 is between S and T

What does the tern between in the stmt. 2 Mean .. Does that mean exactly in the middle or some where between S and T. Please explain What does between mean in terms of GMAT.

Thanks
-H

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Re: If s and t are two different numbers on the number line, is [#permalink]

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10 May 2013, 09:13
I read between as middle. Isnt the word between confusing???
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Re: If s and t are two different numbers on the number line, is [#permalink]

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13 May 2013, 03:26
Bunuel wrote:
rajathpanta wrote:
I read between as middle. Isnt the word between confusing???

You mean you read "between" as "middle" in "distance between t and 0"? What does it means then?

_________________

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Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

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Re: If s and t are two different numbers on the number line, is [#permalink]

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26 Jun 2013, 08:58
If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t

This one tricked me a bit. For some reason I assumed that "different numbers" could refer to two of the same numbers on the number line (i.e. a=3 and b=3) It was a foolish assumption.

(1) Distance between s and 0 is the same as distance between t and 0

If s and t are different numbers on the number line, but they are equidistant from 0, the only possible arrangement is s=-t or t=-s. For example:

-3 and 3 are different numbers and are equidistant from zero. |s|=|t|
-3 and 4 are different numbers but are NOT equidistant from zero . |s|≠|t|
SUFFICIENT

(2) 0 is between s and t

This tells us nothing about the absolute values of s, t. All it tells us is that s is positive and t is negative or s is negative and t is positive. For example:

-3<0<3 (zero is in between and s+t = 0)
-3<0<4 (zero is in between and s+t ≠ 0)
INSUFFICIENT

(A)

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Re: If s and t are two different numbers on the number line, is [#permalink]

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28 Oct 2014, 05:26
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If s and t are two different numbers on the number line, is [#permalink]

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04 Jun 2015, 10:28
Bunuel wrote:
harikattamudi wrote:
37.If 'S' and 'T' are two different numbers on the number liine, is S + T equal to 0?
(1) The distance between S and 0 is the same as the distance between T and 0.
(2) 0 is between S and T

What does the tern between in the stmt. 2 Mean .. Does that mean exactly in the middle or some where between S and T. Please explain What does between mean in terms of GMAT.

Thanks
-H

0 is between s and t, means 0 is somewhere between s and t on the number line.

If GMAT wants to tell that 0 is exactly between s and t, it would usually state that as "0 is halfway between s and t on the number line", which always can be expressed as $$\frac{s+t}{2}=0$$.

TIPS:
On the GMAT we can often see such statement: $$z$$ is halfway between $$x$$ and $$y$$ on the number line. Remember this statement can ALWAYS be expressed as:

$$\frac{x+y}{2}=z$$.

"The distance between x and y" can always be expressed as $$|x-y|$$.

Hope it helps.

The whole "|x-y| = z" thing remains unsolved for me. If I put x y and z on the number line as following:

x= 1 & y = 5 and if z = midpoint = 3. But |1-5| =/= 3?

What am I missing?

Is |x-y| = z restricted to certain rules?

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Re: If s and t are two different numbers on the number line, is [#permalink]

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15 Oct 2015, 03:58
Bunuel

Since distance between s & 0 is the same as distance between t & 0. I assumed two possibilities: s=8 & t=-8. Both are 8 units away and when added s+t=0. But if s=8 & t=8. Then the sum is 16. So statement 1 should be insufficient. You can correct me.

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Re: If s and t are two different numbers on the number line, is [#permalink]

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17 Oct 2015, 07:36
narendran1990 wrote:
Bunuel

Since distance between s & 0 is the same as distance between t & 0. I assumed two possibilities: s=8 & t=-8. Both are 8 units away and when added s+t=0. But if s=8 & t=8. Then the sum is 16. So statement 1 should be insufficient. You can correct me.

Narendran - the question states that S and T are two different numbers. so S not equal to T.

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Re: If s and t are two different numbers on the number line, is [#permalink]

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17 Oct 2015, 11:55
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If s and t are two different numbers on the number line, is s + t = 0 ?

(1) Distance between s and 0 is the same as distance between t and 0
(2) 0 is between s and t

If we modify the original condition and the question, we want to know whether s=-t.
Looking at condition 1, |s-0|=|t-0|, |s|=|t| and from this we can get s=t or s=-t, but it is given that s and t are different, so s=-t, the answer is 'yes', making this condition sufficient.
For condition 2, the answer to the question becomes 'yes' for s=2, t=-2, but 'no' for s=3,t=-2. This condition is insufficient, and the answer becomes A.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If s and t are two different numbers on the number line, is [#permalink]

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05 Aug 2016, 10:04
Another question where you need to pay attention to the wording, 'different numbers' therefore 1 is sufficient as 0 will have to be inbetween the s and t.
Statement 2 clearly insufficient.

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Re: If s and t are two different numbers on the number line, is [#permalink]

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Re: If s and t are two different numbers on the number line, is   [#permalink] 16 Aug 2017, 19:19
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