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# In the x-y coordinate plane, the distance between (m, n) and (3, 4) is

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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is  [#permalink]

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13 Dec 2016, 00:55
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Difficulty:

55% (hard)

Question Stats:

58% (02:08) correct 42% (02:11) wrong based on 91 sessions

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In the x-y coordinate plane, the distance between (m, n) and (3, 4) is$$√26$$. If m and n are integers, how many possible cases are there?
A. 5 B. 6 C. 7 D. 8 E. 9

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"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" ##### Most Helpful Expert Reply e-GMAT Representative Joined: 04 Jan 2015 Posts: 3074 Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink] ### Show Tags 20 Feb 2017, 23:18 4 2 Nunuboy1994 wrote: I don't understand this question • The distance between any two points in a coordiante plane is given by - o $$(x_1-x_2)^2 + (y_1-y_2)^2 = d^2$$ o where $$d$$ is the distance between the points ($$x_1,y_1$$) and ($$x_2,y_2$$) • In the question, we are given that the distance between ($$m,n$$) and ($$3,4$$) is $$√26$$ • Using the above formula, we can write - o $$(m-3)^2 + (n-4)^2 = (√26)^2$$ o $$(m-3)^2 + (n-4)^2 = 26$$ • Since m and n are integers, the value of $$(m-3)^2$$ and $$(n-4)^2$$ will also be integers. o We can write $$(m-3)^2 + (n-4)^2 = 25 + 1$$ o Now there are a number of possibilities - either  $$(m-3)^2 = 25$$ and $$(n-4)^2 = 1$$  which gives us $$m-3 =$$ +$$5$$ or -$$5$$ and $$(n-4) =$$+$$1$$or -$$1$$ • Thus from here we will get 2 possibilities of m and 2 possibilities of n. And the total number of cases possible are $$2 *2 = 4$$ OR • There is also a possibility that $$(m-3)^2 = 1$$ and $$(n-4)^2 = 5$$ o which gives us $$m-3 =$$ +$$1$$ or -$$1$$ and $$n-4 =$$ +$$5$$ or -$$5$$ • Thus, from here also there are 2 possibilities each for m and n. And the total number of cases possible are $$2 * 2 = 4$$ • Therefore, the total number of cases possible for ($$m, n$$) are $$4 + 4 = 8$$. Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts _________________ ##### General Discussion Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is [#permalink] ### Show Tags 15 Dec 2016, 01:15 1 ==> From $$(m-3)^2+(n-4)^2$$=(√26)2, you get (m-3, n-4)=(±1, ±5) or (±5, ±1), so there are total of 8 numbers. Therefore, the answer is D. Answer: D _________________ 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"
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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is  [#permalink]

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20 Feb 2017, 19:48
I don't understand this question
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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is  [#permalink]

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16 Oct 2018, 01:53
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Re: In the x-y coordinate plane, the distance between (m, n) and (3, 4) is   [#permalink] 16 Oct 2018, 01:53
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