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If X = 27^324 and Y = 3^134, what is the units digit of X/Y?

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If X = 27^324 and Y = 3^134, what is the units digit of X/Y?  [#permalink]

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New post 28 Apr 2016, 00:16
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E

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  55% (hard)

Question Stats:

65% (01:15) correct 35% (01:26) wrong based on 226 sessions

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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?  [#permalink]

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New post 28 Apr 2016, 01:23
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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?  [#permalink]

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New post 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 3^838

since 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?  [#permalink]

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New post 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?  [#permalink]

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New post 13 Jan 2019, 04:13
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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 \(=4\).

\(\frac{3^{972}}{3^{134}}\) \(\implies\) \(3^{972-134}\) \(\implies\) \(3^{838}\) \(\implies\) unit digit \(=9\)

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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?  [#permalink]

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New post 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^(972-134) = 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?  [#permalink]

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New post 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 Nn2

We 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?  [#permalink]

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New post 17 Jan 2019, 10:10
27^324/3^134 unit place
Now 27=3^3 so x/Y =3^(972-134)=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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Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y? &nbs [#permalink] 17 Jan 2019, 10:10
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If X = 27^324 and Y = 3^134, what is the units digit of X/Y?

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