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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
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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]  23 Jun 2020, 13:42
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Expert's post
If we think of XY and XZ as 2 sides of a triangle, we can use the following rule to find the range of values for YZ:

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

When we apply this property, we get: 8 < YZ < 32

ASIDE: This looks a lot like answer choice B, except B features "less than or equal to" symbols (≤). The reason we need "≤" is that XYZ need not be a triangle. So, we must also include the possibility that X, Y and Z lie in a straight line.

For this reason, the correct answer is B
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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  23 Jun 2020, 13:43
Expert's post
Thank you for the explanation
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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  26 Jun 2020, 02:15
How can we solve it by placing the points on number line?
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Re: The distance from point X to point Y is 20 miles, and the di [#permalink]  26 Jun 2020, 03:18
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I strongly recommend to you read our book.

There is the chapter about lines, word problem and so forth

If you do not strong theory foundation you will fly always blind

https://greprepclub.com/forum/gre-quant ... tml#p52437

And here https://greprepclub.com/forum/greprepcl ... html#p5077

You need practice but without theory and your skill baseline, you will end up to take 10 times to learn and master something

Regards
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Re: The distance from point X to point Y is 20 miles, and the di   [#permalink] 26 Jun 2020, 03:18
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