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

 It is currently 20 Oct 2019, 19:50

### 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

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

# In the xy-coordinate plane how many circles can be constructed that ha

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58434
In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 00:00
1
3
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:07) correct 51% (02:18) wrong based on 40 sessions

### HideShow timer Statistics

Competition Mode Question

In the xy-coordinate plane how many circles can be constructed that have a center at (r, s), where r and s are integers, that have a radius with an integer length, and that in no portion lie outside the square region defined by $$0 \leq x \leq 5$$ and $$0 \leq y \leq 5$$?

A. 16
B. 20
C. 21
D. 24
E. 25

_________________
SVP
Joined: 03 Jun 2019
Posts: 1734
Location: India
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 00:38
1
Asked: In the xy-coordinate plane how many circles can be constructed that have a center at (r, s), where r and s are integers, that have a radius with an integer length, and that in no portion lie outside the square region defined by 0≤x≤5 and 0≤y≤5?

Let r = 1;
Centers of circle may be at (x,y) where x = {1,2,3,4} and y={1,2,3,4} Total cases = 4 * 4 = 16
Let r =2;
Centers of circle may be at (x,y) where x = {2,3} and y={2,3} Total cases = 2 * 2 = 4
Let r=3;
Any circle is NOT POSSIBLE since diameter = 6 >5 and portion of the circles lie outside the given region defined by 0≤x≤5 and 0≤y≤5
Total cases = 16 + 4 = 20

IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Senior Manager
Joined: 07 Mar 2019
Posts: 329
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 04:03
1
First of all, the square is of dimension 5x5 as 0 ≤ x ≤ 5 and 0 ≤ y ≤ 5 and centers of all circles have coordinates as integer values and so are lengths of radii of all the circles.

Now, circles can be of either radius 1 unit or 2 units only since radius of 3 would result in diameter of 6 units whereas as per question no portion of a circle should be outside the square of dimension 5 x 5.

Consider the snapshot as attached.

Here, points except purple color and those on x & y axis can only be centers of circles.
1. Blue points can have length of 1 unit only to suffice the condition. Total blue points = 12 i.e. total circles are 12x1 = 12.
2. Pink points can have length of 1 and 2 units to suffice the condition. Total pink points = 4 i.e. total circles are 4x2 = 8.

Hence total circles are 20.

Attachments

File comment: In the xy-coordinate

In the xy-coordinate.png [ 37.51 KiB | Viewed 519 times ]

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Joined: 18 May 2019
Posts: 365
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 04:04
Given range in the coordinate plane where the circles have to be drawn is 0<=x<=5 and 0<=y<=5.
Radius of each circle must be an integer, the origin of the circle must have cordinates (r,s) where r and s are integers.
Possible radius that can be drawn within a square of sides 5x5 is 1 and 2.

Since the circles must be within the region defined in the coordinate plane, r and r have the following possible integer values
r= {1,2,3, and 4} and s={1,2,3, and 4}.
There are 4*4 =16 circles that can be drawn with a radius of 1 unit.

With a radius of 2, there possible values that r and s can take so that the circle can be drawn within the region defined above, are as follows:
r={2 and 3} and s={2 and 3}
2*2 circles of radius 2 units can be drawn within the region defined above.

Total number of circles = 16+4=20.

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5022
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 06:46
In the xy-coordinate plane how many circles can be constructed that have a center at (r, s), where r and s are integers, that have a radius with an integer length, and that in no portion lie outside the square region defined by 0≤x≤50≤x≤5 and 0≤y≤50≤y≤5?

A. 16
B. 20
C. 21
D. 24
E. 25

I plotted the values and solved with each center
x=1 ; ( 1,1) ( 1,2) ( 1,3) ( 1,4)
x=2 ; ( 2,1) ( 2,2) ( 2,2) ( 2,3) ( 2,3) ( 2,4)
x=3; (3,1) ( 3,2) ( 3,2) ( 3,3) ( 3,3) ( 3,4)
x=4 ; ( 4,1) ( 4,2) ( 4,3) ( 4,4)
radius of lengths will be either 1 or 2
total center points ;20
IMO B
Senior Manager
Joined: 10 Aug 2018
Posts: 335
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 09:00
B 20.

and 4 circles of radius 2.
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"

GMAT:[640 Q44, V34, IR4, AWA5]
Senior Manager
Joined: 10 Sep 2013
Posts: 307
Location: India
GMAT 1: 720 Q50 V38
GPA: 4
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 09:20
An easy one.

we have 16 circles with center (x,y) 1<=X<=4, 1<=Y<=4(subtract 1 from both ends)

WE have 4 circles with center (x,y) 2<=x<=3, 2<=x<=3(Subtract 2 from both ends)

for radius 3, such circle is not possible. Try subtracting 3 in above limit.

Hence total=20.
Manager
Joined: 24 Sep 2014
Posts: 51
Concentration: General Management, Technology
Re: In the xy-coordinate plane how many circles can be constructed that ha  [#permalink]

### Show Tags

26 Aug 2019, 10:28
In the xy-coordinate plane how many circles can be constructed that have a center at (r, s), where r and s are integers, that have a radius with an integer length, and that in no portion lie outside the square region defined by 0≤x≤5 and 0≤y≤5?

The circle should lie within the the square defined by the region 0<=x<=5 & 0<=y<=5
The radius of the circle should be an integer, so the radius value could be 1 or 2
And the center (r, s) are integers, so we can construct circles with radius 1 at center (r, s) as = (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) and with radius 2 and at center (r, s) as = (2,2), (2,3), (3,2), and (3,3)
So, the total number of circles is 20
Re: In the xy-coordinate plane how many circles can be constructed that ha   [#permalink] 26 Aug 2019, 10:28
Display posts from previous: Sort by