On the number line shown, is zero halfway between r and s
<-----------------r---------s----t----------->
1)s is to the right of zero
2)The distance between t and r is the same as the distance between t and -s
In my opinion the answer to this question should be B. However GMAC says that the answer is C.
My reasoning is that, for the distance between rand t to be equal to the distance between t and -s, r should be equal to -s. Therefore statement 2 alone is sufficient to answer this question.
Can someone please explain how the answer is C
On the number line shown, is zero halfway
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r could be equal to -s, but it doesn't need to be, at least not if all three of our unknowns are negative. We could have r = -4, s = -2 and t = -1, for example.utopian_wanderer wrote:On the number line shown, is zero halfway between r and s
<-----------------r---------s----t----------->
1)s is to the right of zero
2)The distance between t and r is the same as the distance between t and -s
In my opinion the answer to this question should be B. However GMAC says that the answer is C.
My reasoning is that, for the distance between rand t to be equal to the distance between t and -s, r should be equal to -s. Therefore statement 2 alone is sufficient to answer this question.
Can someone please explain how the answer is C
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Your reasoning is not totally wrong that "for the distance between r and t to be equal to the distance between t and -s, r should be equal to -s." But you are missing one thing here that it will be true only if we know what type of number (+/-) s is, which we get to know only if we take statement 1 into account also. My answer is CIan Stewart wrote:r could be equal to -s, but it doesn't need to be, at least not if all three of our unknowns are negative. We could have r = -4, s = -2 and t = -1, for example.utopian_wanderer wrote:On the number line shown, is zero halfway between r and s
<-----------------r---------s----t----------->
1)s is to the right of zero
2)The distance between t and r is the same as the distance between t and -s
In my opinion the answer to this question should be B. However GMAC says that the answer is C.
My reasoning is that, for the distance between rand t to be equal to the distance between t and -s, r should be equal to -s. Therefore statement 2 alone is sufficient to answer this question.
Can someone please explain how the answer is C
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Although I am always grateful for Ian’s explanation, I doubt that I would have been able to apply this reasoning on test day. Actually the first time I saw the question, I did not think of the possibility of all three (r, s, & t) being negative.
Is there a more certain (maybe algebraic?) option for solving 2)?
For example, I am sure we could write 2) as
2)The distance between t and r is the same as the distance between t and –s
AB. VALUE ( t – r) = AB. VALUE ( t + s)
(Read : t-r between absolute value bars and t+s between absolute value bars)
Is there an algebraic way from here that might lead to ‘Insufficient’?
Is there a more certain (maybe algebraic?) option for solving 2)?
For example, I am sure we could write 2) as
2)The distance between t and r is the same as the distance between t and –s
AB. VALUE ( t – r) = AB. VALUE ( t + s)
(Read : t-r between absolute value bars and t+s between absolute value bars)
Is there an algebraic way from here that might lead to ‘Insufficient’?
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I'd suggest beginning by imagining the possible locations of zero on the number line shown. When we consider statement 2 alone, we know that -s is just the reflection of s through zero on the number line. Certainly s could be to the right of zero, and zero could be halfway between r and s:jeemat wrote:Can anyone explain how this can be accomplished in 2 minutes? Or like they asked above, how they would structure their work?
---r---0---s---t---
so we just need to see if it's possible that s is to the left of zero. Indeed it is possible, provided all of our numbers are negative:
--r--s--t--0--(-s)-----
When I consider this latter possibility, I just imagine values for r, t and -s so that t is in the middle - for example -6, -1, 4, (so s = -4) or -10, -2, 6 (so s = -6). It's certainly feasible to imagine one of these scenarios within two minutes, provided you look at the problem in a suitable way early on.
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Solution:utopian_wanderer wrote: ↑Sun Jan 18, 2009 11:08 amOn the number line shown, is zero halfway between r and s
<-----------------r---------s----t----------->
1)s is to the right of zero
2)The distance between t and r is the same as the distance between t and -s
We need to determine whether zero halfway between r and s. We see that 0 could be in one of the following four places: 1) to the left of r, 2) between r and s, 3) between s and t, 4) to the right of t. We will refer to these four cases as cases 1, 2, 3 and 4, respectively.
Statement One Only:
s is to the right of zero.
This tells us s is positive; however, without knowing anything about r, we can’t determine whether they are opposites. Statement one is not sufficient to answer the question.
Statement Two Only:
The distance between t and r is the same as the distance between t and -s.
We see that it can’t be case 1 or 3 since the former case has t further away from -s than it’s from r whereas the latter case has t further away from r than it’s from s. However, it can still be either case 2 or 4. If it’s the former, then yes, not only 0 is between r and s, 0 is exactly halfway between r and s. However, if it’s the latter, then no, because both r and s are less than 0. Statement two is not sufficient to answer the question.
Statements One and Two Together:
From statement two, we know it’s either case 2 or 4. However, since from statement one, s is positive, then it must be case 2 (since this case has s positive) and not case 4 (since this case has s negative). From the analysis for statement two, we see that if it is case 2, then 0 is exactly halfway between r and s. The two statements together are sufficient to answer the question.
Answer: C
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