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

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If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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Updated on: 14 Feb 2019, 00:40
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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

Originally posted by LM on 27 Apr 2010, 10:04.
Last edited by Bunuel on 14 Feb 2019, 00:40, edited 1 time in total.
Renamed the topic.
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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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27 Apr 2010, 10:51
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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 s + t = 0  [#permalink]

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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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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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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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Re: If s and t are two different numbers on the number line, is s + t = 0  [#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 s + t = 0  [#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 s + t = 0  [#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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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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28 Oct 2014, 05:26
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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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17 Oct 2015, 11:55
1
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 s + t = 0  [#permalink]

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17 Dec 2015, 10:47
1
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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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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04 Dec 2018, 16:03
Hi All,

We're told that S and T are two DIFFERENT numbers on the number line. We're asked if S + T = 0. This is a YES/NO question and can be solved by TESTing VALUES and a bit of Number Property logic.

1) The distance between S and 0 is the SAME as the distance between T and 0

Since S and T are DIFFERENT numbers, the only way for their respective distances from 0 to be the SAME is if S and T are 'opposites.'

IF....
S = +1, T = -1; the distances from 0 are the same and S+T = (1) + (-1) = 0, so the answer to the question is YES
S = -2, T = +2; the distances from 0 are the same and S+T = (-2) + (+2) = 0, so the answer to the question is YES.
Etc.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 0 is between S and T

With the information in Fact 2, we know that 0 is some point between S and T, but that does NOT necessarily mean the "exact midpoint."

IF...
S = +1, T = -1; then S+T = (1) + (-1) = 0, so the answer to the question is YES
S = +1, T = -2; then S+T = (1) + (-2) = -1, so the answer to the question is NO
Fact 2 is INSUFFICIENT

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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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14 Feb 2019, 00:22
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.

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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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13 Jul 2019, 04:56
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

A as it says that s-0=0-t
B is not sufficient , we dont know where actually A and B lie
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Re: If s and t are two different numbers on the number line, is s + t = 0  [#permalink]

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21 Jul 2019, 19:52
"Different" numbers is the only thing that makes A correct, otherwise we could plausibly have s=t
Re: If s and t are two different numbers on the number line, is s + t = 0   [#permalink] 21 Jul 2019, 19:52
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