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Math Expert V
Joined: 02 Sep 2009
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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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Difficulty:   55% (hard)

Question Stats: 66% (01:39) correct 34% (01:52) wrong based on 256 sessions

### HideShow timer Statistics 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

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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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2
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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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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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?
Manager  B
Joined: 03 Sep 2018
Posts: 63
If X = 27^324 and Y = 3^134, what is the units digit of X/Y?  [#permalink]

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2
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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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

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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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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 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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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 Re: If X = 27^324 and Y = 3^134, what is the units digit of X/Y?   [#permalink] 17 Jan 2019, 11:10
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