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Math Revolution GMAT Instructor
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In the xy coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]
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12 Dec 2016, 23:55
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In the xy 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82

Re: In the xy coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]
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15 Dec 2016, 00:15
==> From \((m3)^2+(n4)^2\)=(√26)2, you get (m3, n4)=(±1, ±5) or (±5, ±1), so there are total of 8 numbers. Therefore, the answer is D. Answer: D
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Re: In the xy coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]
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20 Feb 2017, 18:48
I don't understand this question



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Re: In the xy coordinate plane, the distance between (m, n) and (3, 4) is [#permalink]
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20 Feb 2017, 22:18
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Nunuboy1994 wrote: I don't understand this question • The distance between any two points in a coordiante plane is given by 
o \((x_1x_2)^2 + (y_1y_2)^2 = d^2\) 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 \((m3)^2 + (n4)^2 = (√26)^2\) o \((m3)^2 + (n4)^2 = 26\) • Since m and n are integers, the value of \((m3)^2\) and \((n4)^2\) will also be integers.
o We can write \((m3)^2 + (n4)^2 = 25 + 1\) o Now there are a number of possibilities  either
\((m3)^2 = 25\) and \((n4)^2 = 1\) which gives us \(m3 =\) +\(5\) or \(5\) and \((n4) =\)+\(1\)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 \((m3)^2 = 1\) and \((n4)^2 = 5\)
o which gives us \(m3 =\) +\(1\) or \(1\) and \(n4 =\) +\(5\) 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 eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Re: In the xy coordinate plane, the distance between (m, n) and (3, 4) is
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