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# What is the greatest possible straight-line distance, in centimeters,

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What is the greatest possible straight-line distance, in centimeters, [#permalink]

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04 Dec 2017, 22:03
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Question Stats:

71% (00:57) correct 29% (01:12) wrong based on 17 sessions

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What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:

2017-12-05_0959_001.png [ 6.06 KiB | Viewed 405 times ]
[Reveal] Spoiler: OA

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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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04 Dec 2017, 22:14
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

Bottom Plane to calculate the Hypotenuse
$$10^2 + 20^2 = 500$$
$$Hypo = 10\sqrt{5}$$

Plane parallel to Height
$$B = 10\sqrt{2}$$
$$Height = 10$$
$$Hypo = \sqrt{(100 + 500)} = 10\sqrt{6}$$
C
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Luckisnoexcuse

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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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05 Dec 2017, 10:03
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

Is 20 cm correctly placed?

I feel like 20 cm and 10 cm are referring to same length

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

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What is the greatest possible straight-line distance, in centimeters, [#permalink]

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05 Dec 2017, 10:28
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

The longest straight-line distance in a right rectangular prism (a rectangular box) is between two opposite corners of the box.

If the measurements of the box are $$x, y, z$$, then the distance between two opposite corners, often called a "space diagonal," $$d$$, is

$$\sqrt{x^2 + y^2 + z^2}$$

Here, $$10^2 + 10^2 + 20^2 = d^2$$
$$600 = d^2$$
$$d = \sqrt{100 * 6} = 10\sqrt{6}$$

lesner19 , I agree, one measurement is mismarked. Whether you use one step or two to get the length of the space diagonal, though, the answer is the same because both depend on three distinct lengths.
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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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05 Dec 2017, 10:45
Formula for the diagonal of a rectangular box is always:

$$\sqrt{a^2+b^2+c^2}$$

Therefore it is just -

= $$\sqrt{10^2 + 10^2 + 20^2}$$

= $$\sqrt{100 + 100 + 400}$$

= $$\sqrt{600}$$

= 10$$\sqrt{6}$$
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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:12
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks

Kudos [?]: 57 [0], given: 511

Math Expert
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Posts: 43348

Kudos [?]: 139643 [0], given: 12794

Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:16
KS15 wrote:
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks

Yes, 10, 10 and 20 are width, breadth and length of the rectangle.
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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:21
Bunuel wrote:
KS15 wrote:
Bunuel wrote:

What is the greatest possible straight-line distance, in centimeters, between two vertices of the rectanglar box shown above?

(A) 10√2
(B) 10√5
(C) 10√6
(D) 30
(E) 40

[Reveal] Spoiler:
Attachment:
2017-12-05_0959_001.png

Bunuel-I think bottom 10 and top 20 reflect the same length and are incorrectly placed-can you please confirm/correct?

Thanks

Yes, 10, 10 and 20 are width, breadth and length of the rectangle.

I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

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Math Expert
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Posts: 43348

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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:23
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.
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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:28
Bunuel wrote:
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.

Well if it were clear, then 2 people would not be raising this point-Also, I wasted a few minutes trying to figure out how the width can be both 10 and 20-so it is certainly not obvious .

Kudos [?]: 57 [0], given: 511

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139643 [0], given: 12794

Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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15 Dec 2017, 01:30
KS15 wrote:
Bunuel wrote:
KS15 wrote:
I think you did not understand my point-please see the figure. Bottom 10 and top 20 seem to reflect the same dimensions whereas they should be different.

It's clear that the figure has a typo in it but it's obvious what the question means.

Well if it were clear, then 2 people would not be raising this point-Also, I wasted a few minutes trying to figure out how the width can be both 10 and 20-so it is certainly not obvious .

Archived the question. Thank you very much for valuable input.
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Re: What is the greatest possible straight-line distance, in centimeters,   [#permalink] 15 Dec 2017, 01:30
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