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M09-34

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Bunuel
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M09-34 [#permalink] New post   16 Sep 2014, 00:40
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If A, B, and C are distinct points on the number line, is the length of segment AB less than 10 units?


(1) The combined length of segments AC and BC equals 10 units.

(2) The combined length of segments AB and AC is more than 10 units.
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Bunuel
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Re M09-34 [#permalink] New post   16 Sep 2014, 00:41
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Official Solution:


Even when combining both statements, we cannot arrive at a definitive answer. Observe the two examples provided below:




Answer: E
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Re: M09-34 [#permalink] New post   07 Apr 2016, 14:31
Hi, I Have a Question. I May be missing something but, when we take both statements together isn't it enough to answer the question because if AC + BC must = 10 and Also AC + AB must be More than 10 ? ( that is don't we need the same set of points to satisfy both statement, here we take 2 different set of points but the second set dose not satisfy both statements. Therefore I believe that because only the first statement satisfies both statements and it = 10 we should be able to say that it is not greater than 10. Please let me know if I am missing something. Thank you.
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Re: M09-34 [#permalink] New post   08 Apr 2016, 07:42
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megha4567 wrote:
Hi, I Have a Question. I May be missing something but, when we take both statements together isn't it enough to answer the question because if AC + BC must = 10 and Also AC + AB must be More than 10 ? ( that is don't we need the same set of points to satisfy both statement, here we take 2 different set of points but the second set dose not satisfy both statements. Therefore I believe that because only the first statement satisfies both statements and it = 10 we should be able to say that it is not greater than 10. Please let me know if I am missing something. Thank you.


If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?


(1) The sum of the lengths of line segments AC and BC is 10

(2) The sum of the lengths of line segments AB and AC is more than 10




WHY doesn't the second set satisfy both statements?

BC = 2
AB = 6
AC = 6 + 2 = 8

(1) The sum of the lengths of line segments AC and BC is 10 --> AC + BC = 8 + 2 = 10.

(2) The sum of the lengths of line segments AB and AC is more than 10 --> AB + AC = 6 + 8 = 14 > 10.
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Re: M09-34 [#permalink] New post   16 May 2016, 07:16
so since the question does not specify that the points are in the order a,b, then c.. one cannot make this assumption?
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Re: M09-34 [#permalink] New post   16 May 2016, 07:41
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grainflow wrote:
so since the question does not specify that the points are in the order a,b, then c.. one cannot make this assumption?


Yes, if the order is not specified you cannot assume that there is any particular one.
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RenanBragion
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Re: M09-34 [#permalink] New post   23 Jun 2020, 04:12
I think this is a high-quality question.
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Re: M09-34 [#permalink] New post   15 Aug 2023, 02:31
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M09-34 [#permalink]
15 Aug 2023, 02:31
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