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# If Town A is 300 kilometers due east of Town B, and Town C is 400

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Math Expert
Joined: 02 Sep 2009
Posts: 55148
If Town A is 300 kilometers due east of Town B, and Town C is 400  [#permalink]

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09 Aug 2017, 03:40
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Difficulty:

15% (low)

Question Stats:

100% (00:42) correct 0% (00:00) wrong based on 31 sessions

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If Town A is 300 kilometers due east of Town B, and Town C is 400 kilometers due south of Town B, then the shortest distance, in kilometers, from Town A to Town C is

(A) 450
(B) 500
(C) 550
(D) 600
(E) 700

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Re: If Town A is 300 kilometers due east of Town B, and Town C is 400  [#permalink]

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09 Aug 2017, 04:02
Imo B

The question can be solved by Pythagoras Theorem
The shortest distance is sqrt(90000+160000)=500
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Re: If Town A is 300 kilometers due east of Town B, and Town C is 400  [#permalink]

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09 Aug 2017, 09:12
Bunuel wrote:
If Town A is 300 kilometers due east of Town B, and Town C is 400 kilometers due south of Town B, then the shortest distance, in kilometers, from Town A to Town C is

(A) 450
(B) 500
(C) 550
(D) 600
(E) 700
Attachment:

Untitled.jpg [ 8.93 KiB | Viewed 507 times ]

Now, the shortest distance between A and C is $$\sqrt{400^2 + 300^2}$$ = $$500$$

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If Town A is 300 kilometers due east of Town B, and Town C is 400  [#permalink]

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09 Aug 2017, 16:23
Bunuel wrote:
If Town A is 300 kilometers due east of Town B, and Town C is 400 kilometers due south of Town B, then the shortest distance, in kilometers, from Town A to Town C is

(A) 450
(B) 500
(C) 550
(D) 600
(E) 700

This is a 3-4-5 right triangle, almost no calculation needed.

The lengths 300 and 400 are the legs of a right triangle in 3-4-5 ratio, with an easy multiplier of 100. The hypotenuse or distance between A and C is 500.

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If Town A is 300 kilometers due east of Town B, and Town C is 400   [#permalink] 09 Aug 2017, 16:23
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