The distance from point A to point B is 15 meters, and the

Question

The distance from point A to point B is 15 meters, and the distance from point A to point C is 11 meters. If d is the distance, in meters, between points B and C, then which of the following must be correct?

A. 0 < d < 24
B. 1 < d < 25
C. 2 < d < 26
D. 3 < d < 27
E. 4 < d < 28

A. 0 < d < 24
B. 1 < d < 25
C. 2 < d < 26
D. 3 < d < 27
E. 4 < d < 28

Bunuel · Accepted Answer

The distance from point A to point B is 15 meters, and the distance from point A to point C is 11 meters. If \(d\) is the distance, in meters, between points B and C, which of the following must be correct?

A. \(0 < d < 24\)
B. \(1 < d < 25\)
C. \(2 < d < 26\)
D. \(3 < d < 27\)
E. \(4 < d < 28\)

If point C is on line AB, between points A and B, then the distance between B and C will be 15 - 11 = 4 meters (the least possible distance).

If point C is on line AB, to the left of point A, then the distance between B and C will be 15 + 11 = 26 meters (the greatest possible distance).

Therefore, \(4 \le BC \le 26\). The correct option must cover this entire range. Only option D offers a range that includes all possible values of BC.

Answer: D.

Show Spoiler

Attachment:

M31-51.png [ 1.66 KiB | Viewed 18769 times ]

ILoseUGain · Answer

I don't get this. Distance between C and B will be shortest, if both these points are on the same side of point A. Distance will be the farthest, if B and C are on opposite side of point A.

so d should be between, 4 and 26. Not sure which option to choose now!

chanakya84 · Answer

Yes. I also arrived at d between 4 and 26. Going by the options given I would go for D.

Temurkhon · Answer

point C can be either in line between A and B, opposite direction of B or out of this line, in this case, we get triangle ABC. If it is in line AB then BC=4 meters, if opposite direction, then BC=26 meters, if out of line BC should be less than AB+AC<26 meters. So, maximum BC is less than 26. I think it is C

aniteshgmat1101 · Answer

The distance has to vary between 4 and 26 depending upon whether B and C fall on the same side of A or they are on the opposite sides of A. The sequence could be A----B----C or B----A----C. From the former case we get least distance between B and C = 4 and from the later we get max distance as 38. So, I would go for D, as 3< d < 27 means 4<= d <=26

PareshGmat · Answer

Answer = C. 2 < d < 26

Addition of 2 sides of a triangle has to be MORE than the 3rd side

d has to be less than 26

himanshujovi · Answer

Bunuel my thought process...

There are three possibilities

a) Point C is between A and B .. In that case d = 15 - 11 = 4m

b) Point C is aware from A and B but on same line . In that case d = 15 + 11 = 26m

c) Point C is any arbitrary point thus forming a triangle ABC . Now sum of 2 sides should be greater than third side. So d < 26m. So possible values look like 4 < d<26...

None of the option and now I am confused

WoundedTiger · Answer

Untitled.png Here's is my take We have 3 cases here as you pointed out. Now which range covers all the 3 options should be the answer. Going by that logic, Ans should be D cause we don't which case are we looking at so Correct answer will cover all the possible options.

Bunuel · Answer

Let me ask you a question: doesn't option D covers all the possible values of d?

aimtoteach · Answer

Hello  Bunuel ,

In the case where the lines form a triangle, option D will include 26 too - isnt this wrong?

The third side of the triangle should be between difference of two ( 15-11) and summation of two (11+15).

Am I doing something wrong?

Bunuel · Answer

Who said that A, B and C must form a triangle?

ajdse22 · Answer

Bunnuel,

Are you saying essentially that they can form a triangle and can also be on the same straight line?
So If they are on the same line then either d=4 or d=26. 
But if they are on a triangle then d> 4 and d<26.
 And so combining the two possibilities, we get 4<=d<=26

Bunuel · Answer

Yes, the points can be on the same line. Check here: the-distance-from-point-a-to-point-b-is-15-meters-and-the-169750.html#p1540270

ShashankDave · Answer

It's between 4 and 26 inclusive. But I think it must be given in the question that d is an integer. Only then D stands

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The distance from point A to point B is 15 meters, and the

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

GMAT Problem Solving (PS) Questions

The distance from point A to point B is 15 meters, and the

Prep Toolkit

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