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Points Q, R and S lie in a plane. If the distance between
[#permalink]
21 Sep 2020, 04:40

Expert Reply

Question Stats:

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?

Indicate all such values.

A. 6

B. 7

C. 11

D. 13

E. 28

F. 29

G. 30

320 GRE Math Problems

Indicate all such values.

A. 6

B. 7

C. 11

D. 13

E. 28

F. 29

G. 30

320 GRE Math Problems

Re: Points Q, R and S lie in a plane. If the distance between
[#permalink]
21 Sep 2020, 04:41

Expert Reply

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.

Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

For more theory and practice see our GRE - Math Book

Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

For more theory and practice see our GRE - Math Book

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Joined: **23 Dec 2019 **

Posts: **50**

Concentration: **Finance, Economics**

GMAT 1: **690 Q47 V38**

Re: Points Q, R and S lie in a plane. If the distance between
[#permalink]
24 Sep 2020, 21:48

R....(11).......S...(7).......Q. Since S in middle and the distance between R&Q is 18, The distance between Q&S =18-11=7

or , R....(18).......Q.....(11)....S. Since S is in one side and the distance between R&Q is 18, The distance between Q&S = 18+11=29

My answer is 7 & 29

or , R....(18).......Q.....(11)....S. Since S is in one side and the distance between R&Q is 18, The distance between Q&S = 18+11=29

My answer is 7 & 29

Re: Points Q, R and S lie in a plane. If the distance between
[#permalink]
25 Sep 2020, 02:53

Ok it was a tricky one.

Why do we have to consider all the values in range? I know the min and max range and I selected only those options too but my answer is incorrect

_________________

Why do we have to consider all the values in range? I know the min and max range and I selected only those options too but my answer is incorrect

_________________

Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!

Re: Points Q, R and S lie in a plane. If the distance between
[#permalink]
26 Sep 2020, 07:42

1

Case 1:

Consider all points lie in the same straight line. Then you have two option, 18 - 11 = 7 as minimum length, and 18 + 11 = 29 as maximum length.

Case 2:

Consider these 3 points makes a triangle in the plane. Then all the answer values between the minimum and maximum range are also valid answers.

So, correct answers should be

Consider all points lie in the same straight line. Then you have two option, 18 - 11 = 7 as minimum length, and 18 + 11 = 29 as maximum length.

Case 2:

Consider these 3 points makes a triangle in the plane. Then all the answer values between the minimum and maximum range are also valid answers.

So, correct answers should be

Show: ::

B, C, D, E, F

Re: Points Q, R and S lie in a plane. If the distance between
[#permalink]
26 Sep 2020, 09:52

2

Expert Reply

Carcass 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?

Indicate all such values.

A. 6

B. 7

C. 11

D. 13

E. 28

F. 29

G. 30

Indicate all such values.

A. 6

B. 7

C. 11

D. 13

E. 28

F. 29

G. 30

Here's a sketch of what we're dealing with:

This question is testing your knowledge of the following rule;

If two sides of a triangle have lengths A and B, then . . .

DIFFERENCE between A and B < length of third side < SUM of A and B

This means we can write: 18 - 11 < x < 18 + 11

Simplify: 7 < x < 29

IMPORTANT: The correct answer here WOULD be C, D, E IF we were told that points Q, R and S create a triangle.

However, since we're not told the points create a triangle, it's also possible that all three points are on the same line, in which case we can also get 7 and 29 as possible lengths of RS

For example, if all three points are on a line as follows...

... QS has length 29

And if all three points are on a line like this...

... QS has length 7

Answer: B, C, D, E, F

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