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

Question

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.

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.

KarishmaB · Answer

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

sandysilva · Answer

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

rocko911 · Answer

How do we know that triplet will be like that?

RashmiT · Answer

can you please explain how you got 12 and 13 for other 2 sides?

hwgmat2015 · Answer

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

septwibowo · Answer

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?

rocko911 · Answer

Hypotenuse is always the longest side in a RIGHT TRIANGLE

septwibowo · Answer

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.

Sent from my iPhone using  GMAT Club Forum mobile app

rocko911 · Answer

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

BrentGMATPrepNow · Answer

At the risk of being  that guy , I believe the answer is E. Here's why:

We already know that, if we start at a place on the equator and walk 40,000 km (the approximate circumference of Earth) due east, we will end up at the  same place  we started. 
If we start at a place further north (say Los Angeles) and walk due east, we will return to our starting place in  less than 40,000 
In fact, the further north we move our starting point, the less the distance one must walk due east to return to the starting point.

So, there must exist a point (very close to the North Pole) where, if we walk due east, we will return to our starting place in 5 miles. 
Let's call this point Point Q. 
To reiterate, if we start at Point Q and walk due east for 5 miles, we end up at the exact point we started (Point Q).

So, if we start at a point that is   6  miles due south of Point Q , then Michael's journey goes like this: 
Michael drives  6  miles due north at arrives at Point A (aka Point Q). He then heads due east for 5 miles (at which point, he arrives back at Point Q) . Finally, he drives 6 miles in a straight line (due south) until he reaches his starting point.

So, the length of the 3 legs of his journey are: 5 miles, 6 miles and 6 miles (the shortest leg being 5 miles) 
So, the total trip was 17 miles.

Of course, there's also the option where the total trip is 30 miles.

Since we cannot definitively answer the question,   the correct answer must be E

Cheers,
Brent

dehumaniser · Answer

the shortest leg = 5
z=hypotenuse
x=3rd side

5^2+x^2=z^2
25=z^2-x^2
25=(z-x)(z+x)

z-x=25 or z+x=25
z=25-x or z=25+x

30 is ruled out and cannot be 5 as doesn't satisfy Pythagoras theorem. The only option left is 12.

Hence b=12

dehumaniser · Answer

Is this within the scope of GMAT?

BrentGMATPrepNow · Answer

Ha! 
Most definitely not!

bumpbot · Answer

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

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