M09-34

Question

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.

Bunuel · Answer

Official Solution:

Even when combining both statements, we cannot arrive at a definitive answer. Observe the two examples provided below:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m09-34.png

Answer: E

megha4567 · Answer

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.

Bunuel · Answer

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

https://gmatclub.com/tests-beta/resources/import/img/m09-34.png

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.

grainflow · Answer

so since the question does not specify that the points are in the order a,b, then c.. one cannot make this assumption?

Bunuel · Answer

Yes, if the order is not specified you cannot assume that there is any particular one.

RenanBragion · Answer

I think this is a  high-quality  question.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M09-34

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards