GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Dec 2018, 20:05

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
P
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Reviews Badge
Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Jul 2017, 22:04
7
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (01:48) correct 49% (01:22) wrong based on 214 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.

_________________

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
User avatar
P
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Jul 2017, 22:39
3
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
avatar
G
Joined: 30 Dec 2016
Posts: 230
GMAT 1: 650 Q42 V37
GPA: 4
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 26 Aug 2017, 21:01
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


____________
Please appreciate the efforts by pressing +1 KUDOS (:

Manager
Manager
avatar
B
Joined: 11 Feb 2017
Posts: 189
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 26 Aug 2017, 22:44
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
Intern
avatar
B
Joined: 14 Jul 2017
Posts: 16
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Aug 2017, 01:31
can you please explain how you got 12 and 13 for other 2 sides?
Manager
Manager
avatar
S
Joined: 12 Mar 2015
Posts: 89
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

New post 27 Aug 2017, 07:02
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
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 237
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Premium Member Reviews Badge
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Aug 2017, 07:39
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
Manager
avatar
B
Joined: 11 Feb 2017
Posts: 189
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Aug 2017, 08:27
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
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 237
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Premium Member Reviews Badge
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Aug 2017, 09:00
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
Manager
avatar
B
Joined: 11 Feb 2017
Posts: 189
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 27 Aug 2017, 09:10
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
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3235
Location: Canada
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 24 Aug 2018, 16:06
1
Top Contributor
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.


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
_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
Joined: 29 Sep 2018
Posts: 3
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 23 Nov 2018, 16:26
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
Intern
Intern
avatar
Joined: 29 Sep 2018
Posts: 3
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 23 Nov 2018, 16:30
GMATPrepNow 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.


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



Is this within the scope of GMAT? :cool:
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3235
Location: Canada
Re: Michael drives x miles due north at arrives at Point A. He then heads  [#permalink]

Show Tags

New post 23 Nov 2018, 18:13
Top Contributor
1
dehumaniser wrote:
Is this within the scope of GMAT? :cool:


Ha!
Most definitely not!
_________________

Test confidently with gmatprepnow.com
Image

GMAT Club Bot
Re: Michael drives x miles due north at arrives at Point A. He then heads &nbs [#permalink] 23 Nov 2018, 18:13
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.