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

 It is currently 26 Jun 2019, 03:36

### 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

# The equation of a circle in the x-y coordinate plane is x^2+y^2=25.

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7501
GMAT 1: 760 Q51 V42
GPA: 3.82
The equation of a circle in the x-y coordinate plane is x^2+y^2=25.  [#permalink]

### Show Tags

29 Nov 2018, 02:47
1
4
00:00

Difficulty:

75% (hard)

Question Stats:

50% (01:34) correct 50% (01:45) wrong based on 60 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

The equation of a circle in the $$x-y$$ coordinate plane is $$x^2+y^2=25$$. How many points of the form ($$a,b$$), where $$a$$ and $$b$$ are integers, lie on this circle?

$$A. 4$$
$$B. 6$$
$$C. 8$$
$$D. 10$$
$$E. 12$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7765 Re: The equation of a circle in the x-y coordinate plane is x^2+y^2=25. [#permalink] ### Show Tags 29 Nov 2018, 04:11 MathRevolution wrote: [Math Revolution GMAT math practice question] The equation of a circle in the $$x-y$$ coordinate plane is $$x^2+y^2=25$$. How many points of the form ($$a,b$$), where $$a$$ and $$b$$ are integers, lie on this circle? $$A. 4$$ $$B. 6$$ $$C. 8$$ $$D. 10$$ $$E. 12$$ Hi.. The equation $$x^2+y^2=25......x^2+y^2=5^2$$ is an equation of a circle with its center at the origin of the coordinates and the radius as 5.. What are the coordinates (a,b) and radius 5.. they are the sides of a right angled triangle with hypotenuse 5.. 3-4-5 is a triplet which we will be looking at so we can have coordinates (|3|,|4|)... here 3 and 4 both can take positive and negative values, so 2*2=4------- (3,4);(-3,4);(-3,-4);(3,-4) similarly four ways for (|4|,|3|) The points (0,5), (0,-5), (5,0) and (-5,0) are other 4 ways. Thus 4+4+4=12 ways E _________________ GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 936 Re: The equation of a circle in the x-y coordinate plane is x^2+y^2=25. [#permalink] ### Show Tags 29 Nov 2018, 07:57 MathRevolution wrote: [Math Revolution GMAT math practice question] The equation of a circle in the $$x-y$$ coordinate plane is $$x^2+y^2=25$$. How many points of the form ($$a,b$$), where $$a$$ and $$b$$ are integers, lie on this circle? $$A. 4$$ $$B. 6$$ $$C. 8$$ $$D. 10$$ $$E. 12$$ $$?\,\,\,:\,\,\,\,\# \,\,\left( {x,y} \right)\,\,\,{\rm{integer}}\,\,{\rm{coordinates}}\,\,{\rm{solutions}}\,\,{\rm{for}}\,\,\,{x^2} + {y^2} = 25$$ $$\left| x \right| = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {0,5} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( {0, - 5} \right)$$ $$\left| x \right| = 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{y^2} = 24 \ne \,\,{\rm{perfect}}\,\,{\rm{square}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}\,\,{\rm{solutions}}\,$$ $$\left| x \right| = 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{y^2} = 21 \ne \,\,{\rm{perfect}}\,\,{\rm{square}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}\,\,{\rm{solutions}}\,\,\,$$ $$\left| x \right| = 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{y^2} = 16\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,\left( {x,y} \right) = \left( {3,4} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( {3, - 4} \right) \hfill \cr \,\,\,{\rm{or}} \hfill \cr \,\,\left( {x,y} \right) = \left( { - 3,4} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( { - 3, - 4} \right) \hfill \cr} \right.$$ $$\left| x \right| = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{y^2} = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,\left( {x,y} \right) = \left( {4,3} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( {4, - 3} \right) \hfill \cr \,\,\,{\rm{or}} \hfill \cr \,\,\left( {x,y} \right) = \left( { - 4,3} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( { - 4, - 3} \right) \hfill \cr} \right.\,\,$$ $$\left| x \right| = 5\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{y^2} = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {5,0} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = \left( { - 5,0} \right)$$ $$? = 12$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7501 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The equation of a circle in the x-y coordinate plane is x^2+y^2=25. [#permalink] ### Show Tags 02 Dec 2018, 19:01 => We need to find all pairs of integers ($$a,b$$) such that $$a^2 + b^2 = 25$$. These are: $$(5,0), (4,3), (3,4), (0,5), (-3,4), (-4,3), (-5,0),(-4,-3), (-3,-4), (0,-5), (3,-4)$$ and $$(4,-3)$$. Thus, there are $$12$$ such points that lie on the circle. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: The equation of a circle in the x-y coordinate plane is x^2+y^2=25.   [#permalink] 02 Dec 2018, 19:01
Display posts from previous: Sort by