Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 14 Oct 2015
Posts: 239
GPA: 3.57

Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Jul 2017, 23:04
4
This post was BOOKMARKED
Question Stats:
50% (02:24) correct 50% (01:25) wrong based on 125 sessions
HideShow timer Statistics
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles? A  5 miles B  12 miles C  25 miles D  30 miles E  Cannot be determined by the information given.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Please hit Kudos if this post helped you inch closer to your GMAT goal. Procrastination is the termite constantly trying to eat your GMAT tree from the inside. There is one fix to every problem, working harder!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8003
Location: Pune, India

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Jul 2017, 23:39
jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. So total distance travelled by him must be 5+12+13 = 30 miles
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 30 Dec 2016
Posts: 144

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
26 Aug 2017, 22:01
VeritasPrepKarishma wrote: jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. Hi is there any alternative way to solve this question ? If No, is it advisable to learn the pythagorean triplets ? But there are so many triplets possible. How is one supposed to solve it under 2 min ?Regards Sandy DA Silva
_________________
Regards SandySilva
____________ Hit kudos if my post helped (:



Manager
Joined: 11 Feb 2017
Posts: 204

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
26 Aug 2017, 23:44
jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. How do we know that triplet will be like that?



Intern
Joined: 14 Jul 2017
Posts: 8

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 02:31
can you please explain how you got 12 and 13 for other 2 sides?



Manager
Joined: 12 Mar 2015
Posts: 102
Concentration: Leadership, Finance
GPA: 3.9
WE: Information Technology (Computer Software)

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 08:02
RashmiT wrote: can you please explain how you got 12 and 13 for other 2 sides? Hi RashmiiT, Pythogoras triplet  3:4:5. So we know shortest cannot be hypotenuse. We have x^2 + 5^2 = z^2. All 3 are integers. By testing various values for x we see that (12)^2 + (5)^2 = (13)^2. So total distance is 12+ 5+ 13= 30



Manager
Joined: 27 Dec 2016
Posts: 233
Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 08:39
VeritasPrepKarishma wrote: jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. So total distance travelled by him must be 5+12+13 = 30 miles Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination. How must we translate this kind of word question?
_________________
There's an app for that  Steve Jobs.



Manager
Joined: 11 Feb 2017
Posts: 204

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 09:27
septwibowo wrote: VeritasPrepKarishma wrote: jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. So total distance travelled by him must be 5+12+13 = 30 miles Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination. How must we translate this kind of word question? Hypotenuse is always the longest side in a RIGHT TRIANGLE



Manager
Joined: 27 Dec 2016
Posts: 233
Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 10:00
rocko911 wrote: septwibowo wrote: VeritasPrepKarishma wrote: [quote="jedit"]Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. So total distance travelled by him must be 5+12+13 = 30 miles Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination. How must we translate this kind of word question? Hypotenuse is always the longest side in a RIGHT TRIANGLE[/quote] Sure, I understand that hypotenuse is the longest side of the triangle. But, we often face similar problem who assume the hypotenuse as a shortcut  so although that is the longest side, we can go from start to finish via hypotenuse rather than via its legs. Sent from my iPhone using GMAT Club Forum mobile app
_________________
There's an app for that  Steve Jobs.



Manager
Joined: 11 Feb 2017
Posts: 204

Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]
Show Tags
27 Aug 2017, 10:10
rocko911 wrote: septwibowo wrote: jedit 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 in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?
A  5 miles
B  12 miles
C  25 miles
D  30 miles
E  Cannot be determined by the information given. Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13. So total distance travelled by him must be 5+12+13 = 30 miles Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination. How must we translate this kind of word question? Hypotenuse is always the longest side in a RIGHT TRIANGLE Sure, I understand that hypotenuse is the longest side of the triangle. But, we often face similar problem who assume the hypotenuse as a shortcut  so although that is the longest side, we can go from start to finish via hypotenuse rather than via its legs. Hypotenuse is definitely a shortcut but when ITS GIVEN THAT THE PATH MAKES A RIGHT TRIANGLE then it means the hypotenuse WILL ALWAYS BE THE LONGEST SIDE If it would not be a right triangle then surely it was hard to tell if Hypotenuse is the longest side or not Thanks




Re: Michael drives x miles due north at arrives at Point A. He then heads
[#permalink]
27 Aug 2017, 10:10






