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# The distance from point X to point Y is 20 miles, and the di

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The distance from point X to point Y is 20 miles, and the di [#permalink]  27 Jun 2018, 10:05
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The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance, in miles, between points Y and Z. then the range of possible values for d is indicated by

(A) $$8 \leq d \leq 20$$

(B) $$8 \leq d \leq 32$$

(C) $$12 \leq d \leq 20$$

(D) $$12 \leq d \leq 32$$

(E) $$20 \leq d \leq 32$$
[Reveal] Spoiler: OA

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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  06 Jul 2018, 06:58
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Carcass wrote:
The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance, in miles, between points Y and Z. then the range of possible values for d is indicated by

(A) $$8 \leq d \leq 20$$

(B) $$8 \leq d \leq 32$$

(C) $$12 \leq d \leq 20$$

(D) $$12 \leq d \leq 32$$

(E) $$20 \leq d \leq 32$$

This is tricky.

This can be considered to a triangle.

XY = 20 ( one side)

XZ = 12 ( second one )

YZ = x (third side).

Now we need to get the value of X.

Third side = $$difference between two sides \leq X \leq sum of two sides$$

$$20 -12 \leq X \leq 20 + 12$$

=> $$8 \leq X \leq 32$$

B.
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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  13 Jul 2018, 02:08
msk0657 wrote:
Carcass wrote:
The distance from point X to point Y is 20 miles, and the distance from point X to point Z is 12 miles. If d is the distance, in miles, between points Y and Z. then the range of possible values for d is indicated by

(A) $$8 \leq d \leq 20$$

(B) $$8 \leq d \leq 32$$

(C) $$12 \leq d \leq 20$$

(D) $$12 \leq d \leq 32$$

(E) $$20 \leq d \leq 32$$

This is tricky.

This can be considered to a triangle.

XY = 20 ( one side)

XZ = 12 ( second one )

YZ = x (third side).

Now we need to get the value of X.

Third side = $$difference between two sides \leq X \leq sum of two sides$$

$$20 -12 \leq X \leq 20 + 12$$

=> $$8 \leq X \leq 32$$

B.

Hi @msk0657,

Please note that in a triangle following inequality holds:

Difference between two sides < Third side < Sum of the two sides.

In the above question, the equal sign will hold when all the points(i.e. x,y, and z) will lie on the straight line.

Thanks.
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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  13 Jul 2018, 05:41
1
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msk0657 wrote:

Third side = $$difference between two sides \leq X \leq sum of two sides$$

B.

I am afraid this is not the triangle rule

The property of triangle states that:-

Triangle Inequality:

which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
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Re: The distance from point X to point Y is 20 miles, and the di   [#permalink] 13 Jul 2018, 05:41
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