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Points Q, R and S lie in a plane. If the distance between Q and R is 1

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Bunuel
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Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   26 Nov 2020, 07:21
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Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


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B
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chetan2u
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   26 Nov 2020, 07:38
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Bunuel wrote:
Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


Project PS Butler


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Given Q................18..............R and R...........11.........S
Two possibilities
1) S is between Q and R
Q......7......S..........11............R
So Q and 7 have a distance of 7.
2) S is on right of R.
en Q................18..............R...........11.........S
So, Q to S is 18+11 or 29

Only II in the given option

B
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   26 Nov 2020, 10:44
Bunuel wrote:
Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


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There are 2 possibilities (So 2 options are possible) -

1. Q____________18__________________R_________11____________S ; \(QS = 19\)

2.Q_______7_________S_________11_______R ; \(QS = 7\)

Thus, Answer must be (B) II. \(29\)
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   29 Nov 2020, 02:06
chetan2u wrote:
Bunuel wrote:
Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


Project PS Butler


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Given Q................18..............R and R...........11.........S
Two possibilities
1) S is between Q and R
Q......7......S..........11............R
So Q and 7 have a distance of 7.
2) S is on right of R.
en Q................18..............R...........11.........S
So, Q to S is 18+11 or 29

Only II in the given option

B


Please correct my understanding question says points lie on the same plain and NOT lie on the same straight line .So how can there be only two possibilities?

Why can't points lie as shown in the figure below:

Attachment:
line vs plain.png
line vs plain.png [ 3.51 KiB | Viewed 2202 times ]
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AnirudhaS
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Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   29 Nov 2020, 02:40
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stne wrote:
chetan2u wrote:
Bunuel wrote:
Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


Project PS Butler


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Given Q................18..............R and R...........11.........S
Two possibilities
1) S is between Q and R
Q......7......S..........11............R
So Q and 7 have a distance of 7.
2) S is on right of R.
en Q................18..............R...........11.........S
So, Q to S is 18+11 or 29

Only II in the given option

B


Please correct my understanding question says points lie on the same plain and NOT lie on the same straight line .So how can there be only two possibilities?

Why can't points lie as shown in the figure below:

Attachment:
line vs plain.png

the points can lie making a traingle as you have correctly shown.
But if you recall we have a theorem which states that sum of any two sides MUST be greater than the 3rd side.
So in Case 1, that is not possible because 6+11<18
And in Case 3, that is also not possible because if they are collinear then the maximum distance =18+11 = 29. So we can never reach 30.

Does this explanation help?
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chetan2u
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   29 Nov 2020, 02:49
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stne wrote:
chetan2u wrote:
Bunuel wrote:
Points Q, R and S lie in a plane. If the distance between Q and R is 18 and the distance between R and S is 11, which of the following values could be the distance between Q and S?

I. 6
II. 29
III. 30

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III


Project PS Butler


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Given Q................18..............R and R...........11.........S
Two possibilities
1) S is between Q and R
Q......7......S..........11............R
So Q and 7 have a distance of 7.
2) S is on right of R.
en Q................18..............R...........11.........S
So, Q to S is 18+11 or 29

Only II in the given option

B


Please correct my understanding question says points lie on the same plain and NOT lie on the same straight line .So how can there be only two possibilities?

Why can't points lie as shown in the figure below:

Attachment:
line vs plain.png


Yes, you are correct with your obsn.
But we have taken the two extremes. Least distance is 7 and farthest is 29.
Only 29 fits in.
I’ll include a sketch in my earlier post for better understanding.
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stne
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   29 Nov 2020, 03:36
AnirudhaS wrote:
stne wrote:

Please correct my understanding question says points lie on the same plain and NOT lie on the same straight line .So how can there be only two possibilities?

Why can't points lie as shown in the figure below:

Attachment:
line vs plain.png

the points can lie making a traingle as you have correctly shown.
But if you recall we have a theorem which states that sum of any two sides MUST be greater than the 3rd side.
So in Case 1, that is not possible because 6+11<18
And in Case 3, that is also not possible because if they are collinear then the maximum distance =18+11 = 29. So we can never reach 30.

Does this explanation help?


Definitely helped. Thank you.
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EgmatQuantExpert
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink] New post   30 Nov 2020, 21:58
Expert Reply

Solution



Given
In this question, we are given that
    • Points Q, R and S lie in a plane
    • QR = 18, and RS = 11

To find
We need to determine
    • QS

Approach and Working out
Q, R and S can be arranged in following ways

    • Case 1: R between Q and S
      o QS = QR + RS = 18 + 11 = 29
    • Case 2: S between Q and R
      o QS = QR - RS = 18 - 11 = 7
    • Case 3: Q between R and S
      o QS = RS - QR = -7 (this case is not possible as the value cannot be negative)

    • Thus, the possible values of QS = 29 or 7
    • Therefore, only II is a possible value

Hence, Option B is the correct answer.

Correct Answer: Option B
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Re: Points Q, R and S lie in a plane. If the distance between Q and R is 1 [#permalink]
30 Nov 2020, 21:58
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