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

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.

Answer: A.
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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.

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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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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yup Silly me. over-read it.

Answer: Option A

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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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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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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

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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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.

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

"Different" numbers is the only thing that makes A correct, otherwise we could plausibly have s=t
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