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# Michael drives x miles due north at arrives at Point A. He

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Michael drives x miles due north at arrives at Point A. He [#permalink]  01 Oct 2017, 22:24
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16% (00:59) correct 83% (00:47) wrong based on 12 sessions
Michael drives x miles due north and arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line till the starting point. If x, y, and z are integers, then how many miles did Michael drive if one of the initial two legs of the journey was 5 miles?

(A) 5 miles

(B) 12 miles

(C) 25 miles

(D) 30 miles

(E) Cannot be determined by the information given.

Kudos for correct solution.
[Reveal] Spoiler: OA

Last edited by chetan2u on 24 Nov 2018, 07:17, edited 1 time in total.
Corrected the Q
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  01 Oct 2017, 23:53
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Bunuel wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles a straight line towards is starting point. If x, y, and z are integers, then how many miles did Michael drive if one of the legs of the journey was 5 miles?

(A) 5 miles

(B) 12 miles

(C) 25 miles

(D) 30 miles

(E) Cannot be determined by the information given.

Kudos for correct solution.

Since it is given that it travel north first , then east and finally meets the starting point so it constitutes a right angle triangle

since x,y,z are integers and 5 is the shortest distance.

Thus we know the sides of the right angle triangle and shortest side 5 is given by 5:12:13

SO the total distance traveled by him is 5+12+13=30. Option D
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  02 Oct 2017, 07:14
pranab01 wrote:
Bunuel wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles a straight line towards is starting point. If x, y, and z are integers, then how many miles did Michael drive if one of the legs of the journey was 5 miles?

(A) 5 miles

(B) 12 miles

(C) 25 miles

(D) 30 miles

(E) Cannot be determined by the information given.

Kudos for correct solution.

Since it is given that it travel north first , then east and finally meets the starting point so it constitutes a right angle triangle

since x,y,z are integers and 5 is the shortest distance.

Thus we know the sides of the right angle triangle and shortest side 5 is given by 5:12:13

SO the total distance traveled by him is 5+12+13=30. Option D

How did you reach the 5:12:13 triple? Just remembered it as one of the primitive Pitagorean triple or are there any kind of computation to use?
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  02 Oct 2017, 10:04
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IlCreatore wrote:

How did you reach the 5:12:13 triple? Just remembered it as one of the primitive Pitagorean triple or are there any kind of computation to use?

Yes they are pythagorean triplets

here are few more -

3 : 4 : 5

5 : 12 : 13

8 : 15 : 17

1 : 1 : √2

1 : √3: 2
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  24 Nov 2018, 01:17
The question states one of the legs of the journey was 5 miles.
We haven't been told which one, the shorter one or the longer one.
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  24 Nov 2018, 02:04
indiragre18 wrote:
The question states one of the legs of the journey was 5 miles.
We haven't been told which one, the shorter one or the longer one.

I agree. This wouldn't be a problem but we also have the answer option of 12, which corresponds to another P. Triple of 3-4-5. We are never told that 5 is the shortest leg of the journey or the longest. If we assume shortest, 5-12-13 works, if we assume longest, 3-4-5 works.

Now, the only possibility I can see here is that "one of the legs of the journey" in the original question directly corresponds to a triangle side that is NOT the hypotenuse, however this wouldn't really make sense as we are never outright told we have a triangle (figuring this out is part of the problem I assume), and classifying the 2 shorter sides as "legs" and the longer hypotenuse as something else also doesn't make sense from a terminology standpoint.
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Re: Michael drives x miles due north at arrives at Point A. He [#permalink]  24 Nov 2018, 07:15
Expert's post
projectoffset wrote:
indiragre18 wrote:
The question states one of the legs of the journey was 5 miles.
We haven't been told which one, the shorter one or the longer one.

I agree. This wouldn't be a problem but we also have the answer option of 12, which corresponds to another P. Triple of 3-4-5. We are never told that 5 is the shortest leg of the journey or the longest. If we assume shortest, 5-12-13 works, if we assume longest, 3-4-5 works.

Now, the only possibility I can see here is that "one of the legs of the journey" in the original question directly corresponds to a triangle side that is NOT the hypotenuse, however this wouldn't really make sense as we are never outright told we have a triangle (figuring this out is part of the problem I assume), and classifying the 2 shorter sides as "legs" and the longer hypotenuse as something else also doesn't make sense from a terminology standpoint.

You are correct in your thinking and even the language is having some typo.
correcting it. Thanks
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: Michael drives x miles due north at arrives at Point A. He   [#permalink] 24 Nov 2018, 07:15
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