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If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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28 Apr 2016, 00:16
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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28 Apr 2016, 01:23
Bunuel wrote: If \(X = 27^{324}\) and \(Y = 3^{134}\), what is the units digit of X/Y?
A. 1 B. 3 C. 5 D. 7 E. 9 Basically it tests pattern : (3,9,7,1) If we take write 27 in terms of 3 and take the dr to the top, it will result in 3^838 since pattern = 4 divide 838/4 and reminder = 2  this points to 9 in the pattern (3,9,7,1)
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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13 Jan 2019, 02:41
Balajikarthick1990 wrote: Bunuel wrote: If \(X = 27^{324}\) and \(Y = 3^{134}\), what is the units digit of X/Y?
A. 1 B. 3 C. 5 D. 7 E. 9 Basically it tests pattern : (3,9,7,1) If we take write 27 in terms of 3 and take the dr to the top, it will result in 3^838since pattern = 4 divide 838/4 and reminder = 2  this points to 9 in the pattern (3,9,7,1) minor correction; it will result in \(3^{972}\)
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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13 Jan 2019, 03:53
My question is on ;What is the units digit of x/y? It doesn't mean x divided by y? Thus it will 9/9 to get the answer 1?



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If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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13 Jan 2019, 04:13
Nn2 wrote: My question is on ;What is the units digit of x/y? It doesn't mean x divided by y? Thus it will 9/9 to get the answer 1? \(3^1=3\), \(3^2=9\), \(3^3=27\), \(3^4=81\) \(\implies\) cyclicity \(=4\). \(\frac{3^{972}}{3^{134}}\) \(\implies\) \(3^{972134}\) \(\implies\) \(3^{838}\) \(\implies\) unit digit \(=9\) Please consider giving Kudos
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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13 Jan 2019, 09:42
Nn2 wrote: My question is on ;What is the units digit of x/y? It doesn't mean x divided by y? Thus it will 9/9 to get the answer 1? but if you solve it in this way x/y = (3^972)/ (3^134) 3^(972134) = 3^838 When you will divide 838/4, you will get remainder 2 This will be the 2nd position in the cyclic pattern of unit digit of 3,9,7,1,3,9,7,1 Answer as E
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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17 Jan 2019, 09:52
Nn2 wrote: My question is on ;What is the units digit of x/y? It doesn't mean x divided by y? Thus it will 9/9 to get the answer 1? Hello Nn2We need to divide the entire number x by entire number y...and not just the units digit of x by units digit of y. Hence if you find the units digit of x, i.e 9, and then units digit of y, i.e 9, and further get final answer as 9/9 = 1, it is incorrect. Take the below example: What is the units digit of remainder of 14/4? The answer is 2. The answer is not 4/4 = 1. Hope this helps.
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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?
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17 Jan 2019, 10:10
27^324/3^134 unit place Now 27=3^3 so x/Y =3^(972134)=3^838 unit place of 3 cycles at 4 power 3,9,7,1 838/4 remainder 2 so 3^2=9 is answer




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