NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 08:55 It is currently 25 Apr 2024, 08:55
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How many points (x y), where x and y are integers, lie inside of the t

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618957 [14]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   05 May 2020, 04:57
14
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

27% (01:51) correct 73% (02:02) wrong based on 74 sessions
Hide Show timer Statistics
How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [5]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   05 May 2020, 07:46
4
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


Are You Up For the Challenge: 700 Level Questions


The step-by-step solution to this HARD problem is explained well in Video

Please subscribe to my YOuTube channel if you wish to watch many such FREE Videos.

Answer: Option A


Attachments

Screenshot 2020-05-05 at 8.14.18 PM.png
Screenshot 2020-05-05 at 8.14.18 PM.png [ 821.43 KiB | Viewed 4682 times ]

General Discussion
User avatar
L
Chethan92
Director
Director
Joined: 18 Jul 2018
Posts: 926
Own Kudos [?]: 1288 [1]
Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy and Utilities)
Send PM
Reviews Badge
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   05 May 2020, 06:53
1
Kudos
Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.
User avatar
P
Kritisood
Director
Director
Joined: 21 Feb 2017
Posts: 521
Own Kudos [?]: 1037 [0]
Given Kudos: 1091
Location: India
GMAT 1: 700 Q47 V39
Send PM
Reviews Badge
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   05 May 2020, 09:26
GMATinsight wrote:
Bunuel wrote:
How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


Are You Up For the Challenge: 700 Level Questions


The step-by-step solution to this HARD problem is explained well in Video

Please subscribe to my YOuTube channel if you wish to watch many such FREE Videos.

Answer: Option A



your videos are really helpful :)
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   06 May 2020, 03:34
1
Kudos
Expert Reply
Kritisood wrote:
GMATinsight wrote:
Bunuel wrote:
How many points (x y), where x and y are integers, lie inside of the triangular region with vertices (0, 0), (0, 31), and (31, 0) ?

A. 435
B. 450
C. 464
D. 465
E. 466


Are You Up For the Challenge: 700 Level Questions


The step-by-step solution to this HARD problem is explained well in Video

Please subscribe to my YOuTube channel if you wish to watch many such FREE Videos.

Answer: Option A



your videos are really helpful :)


Thank you so much Kritisood

I plan to make more such videos. Please subscribe to my YouTube Channel if you have not yet :)
avatar
B
riagarg07
Intern
Intern
Joined: 24 Nov 2019
Posts: 27
Own Kudos [?]: 30 [0]
Given Kudos: 425
Location: India
WE:Analyst (Insurance)
Send PM
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   26 May 2020, 21:13
Chethan92 wrote:
Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.



Hi
Could you please explain the steps as your method seems to be really quick and easy to solve?
Could you please explain the step where you calculated the total points?
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   26 May 2020, 22:23
1
Kudos
Expert Reply
riagarg07 wrote:
Chethan92 wrote:
Mapping the co-ordinates will give a right-angled triangle in the I quadrant.

Since we need to calculate the points inside the triangle, the base will be of length 31-1-1 = 29.
Next line will have 28 points, 27 and so on.

Total points = 29*30/2 = 435.

A is the answer.



Hi
Could you please explain the steps as your method seems to be really quick and easy to solve?
Could you please explain the step where you calculated the total points?


riagarg07

The method explained in short has been well explained in detail in the video. You may watch it for clear understanding.

If you like th evideo then please subscribe to my YouTube channel as well for encouraging me to make more such informative video and for gaining access to many such videos :)
User avatar
B
Kriti1055
Intern
Intern
Joined: 13 Apr 2021
Posts: 7
Own Kudos [?]: 0 [0]
Given Kudos: 93
Send PM
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink] New post   28 Jan 2023, 19:22
Hi Bunuel GMATinsight,

I chose to do the latter part of the question using Combinatorics.

To find the points that lie within the triangular region formed, we use x+y <31

Now, this gives us 15 possible values of x and 15 possible values of y (It is given that x & y are integers) i.e 30 values in total from which any 2 values can be picked (pls note: possible values include integers from 1-15 inclusive)

Using the formula, we get 30C2
Solving: 30!/28!x2!=435

Please let me know whether this way of solving is correct.

Thank you :)
GMAT Club Bot
gmatclubot
Re: How many points (x y), where x and y are integers, lie inside of the t [#permalink]
28 Jan 2023, 19:22
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions