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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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New post 04 Dec 2017, 23:03
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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

Attachment:
2017-12-05_0959_001.png
2017-12-05_0959_001.png [ 6.06 KiB | Viewed 723 times ]


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

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New post 04 Dec 2017, 23:14
Bunuel wrote:
Image
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

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

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New post 05 Dec 2017, 11:03
Bunuel wrote:
Image
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

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

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

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New post 05 Dec 2017, 11:28
Bunuel wrote:
Image
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

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


Answer C

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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New post 05 Dec 2017, 11:45
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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New post 15 Dec 2017, 02:12
Bunuel wrote:
Image
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

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

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New post 15 Dec 2017, 02:16
KS15 wrote:
Bunuel wrote:
Image
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

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 15 Dec 2017, 02:21
Bunuel wrote:
KS15 wrote:
Bunuel wrote:
Image
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

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

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New post 15 Dec 2017, 02:23
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 15 Dec 2017, 02:28
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 .
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Re: What is the greatest possible straight-line distance, in centimeters, [#permalink]

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New post 15 Dec 2017, 02:30
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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New to the Math Forum?
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the greatest possible straight-line distance, in centimeters,   [#permalink] 15 Dec 2017, 02:30
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