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# In the cube shown above, what is the length of diagonal AB?

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Math Expert
Joined: 02 Sep 2009
Posts: 44600
In the cube shown above, what is the length of diagonal AB? [#permalink]

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04 Dec 2017, 23:02
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Difficulty:

15% (low)

Question Stats:

84% (00:14) correct 16% (01:05) wrong based on 45 sessions

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In the cube shown above, what is the length of diagonal AB?

(A) 1
(B) √2
(C) √3
(D) 2√2
(E) 3

[Reveal] Spoiler:
Attachment:

2017-12-05_0959.png [ 6.73 KiB | Viewed 615 times ]
[Reveal] Spoiler: OA

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Joined: 16 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
Re: In the cube shown above, what is the length of diagonal AB? [#permalink]

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05 Dec 2017, 00:22
Bunuel wrote:

In the cube shown above, what is the length of diagonal AB?

(A) 1
(B) √2
(C) √3
(D) 2√2
(E) 3

[Reveal] Spoiler:
Attachment:
2017-12-05_0959.png

$$(one side diagonal)^2 = 1^2 + 1^2 = 2$$
($$Cube's diagonal)^2 = 1^2 + 2 = 3$$ => Hence, $$\sqrt3$$ is the answer
SC Moderator
Joined: 22 May 2016
Posts: 1547
In the cube shown above, what is the length of diagonal AB? [#permalink]

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05 Dec 2017, 09:20
Bunuel wrote:

In the cube shown above, what is the length of diagonal AB?

(A) 1
(B) √2
(C) √3
(D) 2√2
(E) 3

[Reveal] Spoiler:
Attachment:
2017-12-05_0959.png

To find the length of a space diagonal, $$d$$, (corner to corner between non-adjacent faces), use a variation of the Pythagorean theorem:

$$L^2 + H^2 + W^2= d^2$$

$$L = H = W = 1$$

$$L^2 + H^2 + W^2= d^2$$
$$3 = d^2$$
$$d = \sqrt{3}$$

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Formerly genxer123

Intern
Joined: 26 Oct 2017
Posts: 28
Re: In the cube shown above, what is the length of diagonal AB? [#permalink]

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05 Dec 2017, 09:26
Using PGT twice

Diagonal of cube is (side) */root 3/

Imo C

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Intern
Joined: 25 May 2017
Posts: 10
GMAT 1: 750 Q49 V44
Re: In the cube shown above, what is the length of diagonal AB? [#permalink]

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05 Dec 2017, 11:56
Formula for the diagonal of a cube is always:

a$$\sqrt{3}$$ where a is the side

Therefore it is just -

= 1$$\sqrt{3}$$

= $$\sqrt{3}$$

Note: Diagonal-focused questions are *very* common on the GMAT both for cubes and cuboids so memorizing this formula can take you a long way. Diagonals of cubes are also sometimes referred to as "longest distance between two points within a cube".
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Re: In the cube shown above, what is the length of diagonal AB?   [#permalink] 05 Dec 2017, 11:56
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