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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