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

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
The distance from point A to point B is 15 meters, and the  [#permalink]

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03 Apr 2014, 13:22
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75% (hard)

Question Stats:

51% (01:47) correct 49% (01:55) wrong based on 240 sessions

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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

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Posts: 51185
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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20 Jun 2015, 23:54
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Bunuel wrote:
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

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

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

Therefore $$4 \le AC \le 26$$. Correct option must cover this entire range. Only option D offers the range which has all possible values of AC.

Attachment:

M31-51.png [ 1.66 KiB | Viewed 7736 times ]

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Joined: 27 Jan 2014
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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03 Apr 2014, 16:12
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!
Manager
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Posts: 61
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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03 Apr 2014, 19:02
2
Yes. I also arrived at d between 4 and 26. Going by the options given I would go for D.
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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03 Apr 2014, 21:19
Bunuel wrote:
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

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
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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03 Apr 2014, 21:22
1
Bunuel wrote:
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

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
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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04 Apr 2014, 02:38
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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
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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07 May 2014, 02:43
Bunuel wrote:
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

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
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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07 May 2014, 03:08
himanshujovi wrote:
Bunuel wrote:
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

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

Attachment:

Untitled.png [ 14.15 KiB | Viewed 6790 times ]

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.
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Posts: 51185
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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07 May 2014, 03:08
himanshujovi wrote:
Bunuel wrote:
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

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

Let me ask you a question: doesn't option D covers all the possible values of d?
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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22 Jun 2015, 05:11
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?
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Posts: 51185
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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22 Jun 2015, 05:12
aimtoteach wrote:
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?

Who said that A, B and C must form a triangle?
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Posts: 100
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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29 May 2016, 21:51
Bunuel wrote:
aimtoteach wrote:
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?

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

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
Math Expert
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Posts: 51185
Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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30 May 2016, 11:47
ajdse22 wrote:
Bunuel wrote:
aimtoteach wrote:
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?

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

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

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
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Re: The distance from point A to point B is 15 meters, and the  [#permalink]

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16 Nov 2017, 23:15
Bunuel wrote:
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

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
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Re: The distance from point A to point B is 15 meters, and the &nbs [#permalink] 16 Nov 2017, 23:15
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