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Is |s-t|>|s|-|t|?

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Is |s-t|>|s|-|t|?

by Max@Math Revolution » Tue Jan 19, 2016 6:09 pm
Is |s-t|>|s|-|t|?

1) s>t
2) st<0


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by GMATinsight » Wed Jan 20, 2016 6:23 am
Max@Math Revolution wrote:Is |s-t|>|s|-|t|?

1) s>t
2) st<0


* A solution will be posted in two days.
Question : |s-t|>|s|-|t|?

for |s-t|>|s|-|t| to be true the signs of s and t should be same i..e. either both positive or both Negative

Question REPHRASED: Do s and t both have same sign?

Statement 1: s > t
i.e. s may be positive and t may be negative (e.g. s=2 and t=-1)
OR
s and t both may be positive (e.g. s=2 and t=1)
NOT SUFFICIENT

Statement 2: st<0
i.e. one of s and t is Positive and other is Negative
i.e. sand t both have opposite signs
SUFFICIENT

Answer: Option B
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by Max@Math Revolution » Thu Jan 21, 2016 8:49 pm
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.

Is |s-t|>|s|-|t|?
1) s>t
2) st<0

When you modify the original condition and the question, firstly, if |s|<|t|, |s|-|t|<0 -> |s-t|>=0, which is always yes and sufficient. If |s|>=|t|, |s-t|>|s|-|t|>=0. You can square the both equations. Is |s-t|>|s|-|t|?Is (|s-t|)2>(|s|-|t|)2?s2+t2-2st>s2+t2-2|st|? -2st>-2|st|? st<|st|? and st<0?. Therefore, the answer is B.


� 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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by GMATGuruNY » Fri Jan 22, 2016 6:11 am
Max@Math Revolution wrote:Is |s-t|>|s|-|t|?

1) s>t
2) st<0
Statement 1: s > t
Test one case that also satisfies Statement 2.
Case 1: s=1 and t=-1
If we plug this case into |s-t|>|s|-|t|, we get:
|1 - (-1)| > |1| - |-1|
2 > 0.
Here, the answer to the question stem is YES.

Test one case that does NOT also satisfy Statement 2.
Case 2: s=1 and t=0
If we plug this case into |s-t|>|s|-|t|, we get:
|1 - 0)| > |1| - |0|
1 > 1.
Here, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2: st < 0
|s - t| = the DISTANCE BETWEEN S AND T on the number line.
Here, s and t have different signs.
Implication:
s and t must lie on OPPOSITE SIDES OF 0, with the result that the distance between them is equal to the SUM of |s| and |t|:

s<----- |s| ----- 0 ----- |t| ----->t
t<----- |t| ----- 0 ----- |s| ----->s

In each case, the distance between s and t is equal to the SUM of |s| and |t|.
Implication:
The distance between s and t must be GREATER THAN THE DIFFERENCE between |s| and |t|, with the result that |s-t| > |s| - |t|.
SUFFICIENT.

The correct answer is B.
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