lstudentd wrote:
IanStewart Can you help with if this question were to be written differently in two alternative ways as follows?
Alternative question 1:
Is t = |r-s| ?
1) 3r > 3s
2) t = - (r-s)
Alternative question 2:
Is t = |r-s| ?
1) 3r < 3s
2) t = - (r-s)
If you just think about two numbers, like 3 and 7, then when we subtract these two numbers in either order, we get either -4, the negative difference of 3 and 7, or we get 4, the positive difference of 3 and 7. If we take the absolute value after we subtract, though, we always get the positive difference: |3 - 7| = |7 - 3| = 4. That's also the distance between 3 and 7 on the number line. Similarly, when we have two different unknowns r and s, then r-s might be the positive difference of r and s, or it might be the negative difference of r and s. But when we take the absolute value, |r - s| is always the positive difference of r and s. So when a question asks "Is t = |r - s|?", the question is asking "Is t equal to the positive difference of r and s?".
I'll simplify your two Alternative Questions in the obvious ways:
Qn 1:
Is t = |r - s|?
1. r - s > 0
2. t = s- r
Here, Statement 2 tells us "t is either the positive or negative difference of r and s". We don't know which. So we can't answer the question. Using both Statements, we know r-s is the positive difference of r and s. So Statement 2 tells us t is equal to the negative difference or r and s, and if t is negative, there's no chance it equals an absolute value of any kind, let alone the positive difference of r and s, so the answer here is C; using both Statements, we can be certain the answer to the question is 'no'.
Qn 2:
Is t = |r - s|?
1. s - r > 0
2. t = s - r
Similarly, Statement 2 tells us "t is either the positive or negative difference of r and s". That's not sufficient alone, but Statement 1 ensures s-r (not r-s) is the positive difference of s and r, so using both Statements, the answer to the original question must be "yes", and the answer is C. Algebraically, if we know Statement 1 is true, we know s - r = |s - r| = |r - s|, so if t = s - r, then t = |r - s|.
If you wanted to test numbers instead, you'd just need to experiment with two scenarios: one where s > r, and one where r > s, and you'd also find C is the answer to each question.
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