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
OA A
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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
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Given that 's' and 't' are different numbers.
The target question is s+t=0?
Statement 1: 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 distance from 0 to be the same is if 's' and 't' are opposites.
i.e
If s=1, then t=-1, distance from 0 is the same and s+t = 1 + (-1) = 0
If s=2 then t=-2, distance from 0 is the same and s+t = 2 + (-2) = 0
If s=3 then t=-3, distance from 0 is the same and s+t = 3 + (-3) = 0
Therefore, the value of s+t = 0, in all cases; hence, statement 1 is SUFFICIENT.
Statement 2: 0 is between s and t.
This means either 's' or 't' is negative and the other is positive.
If s=1, then t=-1, 0 is between 's' and 't' and s+t = 1 + (-1) = 0
If s=1, then t=-2, 0 is between 's' and 't' and s+t = 1 + (-2) = -1
If s=-3, then t=1, 0 is between 's' and 't' and s+t = -3 + 1 = -2
Since we cannot answer the target question with certainty, therefore, statement 2 is NOT SUFFICIENT.
Since statement 1 alone is SUFFICIENT, then this validates option A as the correct answer.
The target question is s+t=0?
Statement 1: 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 distance from 0 to be the same is if 's' and 't' are opposites.
i.e
If s=1, then t=-1, distance from 0 is the same and s+t = 1 + (-1) = 0
If s=2 then t=-2, distance from 0 is the same and s+t = 2 + (-2) = 0
If s=3 then t=-3, distance from 0 is the same and s+t = 3 + (-3) = 0
Therefore, the value of s+t = 0, in all cases; hence, statement 1 is SUFFICIENT.
Statement 2: 0 is between s and t.
This means either 's' or 't' is negative and the other is positive.
If s=1, then t=-1, 0 is between 's' and 't' and s+t = 1 + (-1) = 0
If s=1, then t=-2, 0 is between 's' and 't' and s+t = 1 + (-2) = -1
If s=-3, then t=1, 0 is between 's' and 't' and s+t = -3 + 1 = -2
Since we cannot answer the target question with certainty, therefore, statement 2 is NOT SUFFICIENT.
Since statement 1 alone is SUFFICIENT, then this validates option A as the correct answer.
