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13 May 2020, 08:16
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E
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Difficulty:
35%
(medium)
Question Stats:
77% (02:11) correct
23%
(02:02)
wrong
based on 60
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What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?
(1) The length, width, and height of the rectangular solid are the squares of prime integers.
(2) The roots of the equation x^2 – 13x = -36 are the width and the height of the rectangular solid.
Are You Up For the Challenge: 700 Level Questions
(1) The length, width, and height of the rectangular solid are the squares of prime integers.
(2) The roots of the equation x^2 – 13x = -36 are the width and the height of the rectangular solid.
Are You Up For the Challenge: 700 Level Questions
13 May 2020, 08:34
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What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?
length^2 + width^2 + height^2 = diagonal^2 where diagonal is the longest straight line between two points in a box/cube.
(1) The length, width, and height of the rectangular solid are the squares of prime integers.
clearly, no values are given. insufficient
(2) The roots of the equation x^2 – 13x = -36 are the width and the height of the rectangular solid.
x^2 – 13x = -36
or,x=4 or 9
since,H < W < L
so,H=4,W=9 but don't know about L insufficient
combining (1) and (2) ,we still don't get value of L .
L may be 25 or 49 insufficient
correct answer E
length^2 + width^2 + height^2 = diagonal^2 where diagonal is the longest straight line between two points in a box/cube.
(1) The length, width, and height of the rectangular solid are the squares of prime integers.
clearly, no values are given. insufficient
(2) The roots of the equation x^2 – 13x = -36 are the width and the height of the rectangular solid.
x^2 – 13x = -36
or,x=4 or 9
since,H < W < L
so,H=4,W=9 but don't know about L insufficient
combining (1) and (2) ,we still don't get value of L .
L may be 25 or 49 insufficient
correct answer E
14 May 2020, 21:49
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Bunuel
The greatest possible distance between any two points on a certain cuboid is always the SPACE DIAGONAL of that solid which is given by:
\sqrt{3} (L^2 + W^2 + H^3)
We need to determine the values of L, W, H.
STATEMENT 1: The length, width, and height of the rectangular solid are the squares of prime integers.
L, W, H can be the squares of any prime integers.
If L = 25, W = 9 and H = 4, we get the value of the space diagonal different than we would get if L = 100, W = 64 and H = 4.
Insufficient
STATEMENT 2: The roots of the equation x^2 – 13x = -36 are the width and the height of the rectangular solid.
x^2 - 13x + 36 = 0
(x - 4) (x - 9) = 0
Thus, H = 4 and W = 9 since H < W (given)
But, we don't know the value of L
Insufficient
COMBINING (1) AND (2)
We have W = 9, H = 4 and L is any square of a prime number greater than 3.
L can be 25 or 100 or 169 or any other sqaure of a prime > 3.
Insufficient
Answer is (E).
