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What is the units digit of 36^y?

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What is the units digit of 36^y?  [#permalink]

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New post 09 Feb 2017, 06:02
11
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

52% (00:49) correct 48% (00:44) wrong based on 221 sessions

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Re: What is the units digit of 36^y?  [#permalink]

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New post 09 Feb 2017, 10:54
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1
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


When does unit digit remain same?

0*0*0..... the unit digit would always remain 0
1*1*1..... the unit digit would always remain 1
5*5*5..... the unit digit would always remain 5
6*6*6..... the unit digit would always remain 6

Stmt-1:
if y > 0 then unit digit will remain 6 as stated above.
Sufficient

Stmt-2:
If y is even then it can be 0,2,4,6...
36^0 = 1
36^2 = 6
Insufficient

Answer is A.

Question is based on following Concepts:
1. Zero is even
2. number^0 = 1 (except number = 0)
3. Unit digit

Pattern: we tend to forget that zero is even and that exponent zero gives the value 1.

In addition Remember:
1^0 = 1 (0 is even)
1^1 = 1 (1 is odd)

Hope this helps :)
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Re: What is the units digit of 36^y?  [#permalink]

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New post 09 Feb 2017, 06:29
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


The unit digit of 6^any integer is always 6

For ex-6^2=36
6^3=216
6^4=1296

So the cycle repeats, remember the cycle of 6 and 1 are always same the unit digit is same respectively.

Now coming back to Que

(A) y is a positive integer==>Unit digit is 6--Sufficient

(B) y is an even integer==>Even or Odd integer doesn't make any difference the unit digit will be 6 hence Sufficient

Hence D
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Re: What is the units digit of 36^y?  [#permalink]

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New post 09 Feb 2017, 11:15
HKD1710 wrote:
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


When does unit digit remain same?

0*0*0..... the unit digit would always remain 0
1*1*1..... the unit digit would always remain 1
5*5*5..... the unit digit would always remain 5
6*6*6..... the unit digit would always remain 6

Stmt-1:
if y > 0 then unit digit will remain 6 as stated above.
Sufficient

Stmt-2:
If y is even then it can be 0,2,4,6...
36^0 = 1
36^2 = 6
Insufficient

Answer is A.

Question is based on following Concepts:
1. Zero is even
2. number^0 = 1 (except number = 0)
3. Unit digit

Pattern: we tend to forget that zero is even and that exponent zero gives the value 1.

In addition Remember:
1^0 = 1 (0 is even)
1^1 = 1 (1 is odd)

Hope this helps :)


Ops I missed 0

Thanks for pointed out!!!

What if in (B)y is an even integer

Y=-2, is this valid?
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Re: What is the units digit of 36^y?  [#permalink]

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New post 13 Feb 2017, 17:15
2
Bunuel wrote:
What is the units digit of 36^y?

(1) y is a positive integer

(2) y is an even integer


We need to determine the units digit of 36^y.

Statement One Alone:

y is a positive integer.

Since the units digit of 36 is 6 and all positive powers of 6 have a units digit of 6, all positive powers of 36 will have a units digit of 6. Statement one alone is sufficient to answer the question.

Statement Two Alone:

y is an even integer.

If y = 0, then 36^0 = 1, which has a units digit of 1. If y = 2, then 36^2 has a units digit of 6. Statement two alone is not sufficient to answer the question.

Answer: A
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Re: What is the units digit of 36^y?  [#permalink]

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New post 19 Feb 2017, 00:26
NandishSS wrote:
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


The unit digit of 6^any integer is always 6

For ex-6^2=36
6^3=216
6^4=1296

So the cycle repeats, remember the cycle of 6 and 1 are always same the unit digit is same respectively.

Now coming back to Que

(A) y is a positive integer==>Unit digit is 6--Sufficient

(B) y is an even integer==>Even or Odd integer doesn't make any difference the unit digit will be 6 hence Sufficient

Hence D

There is one missing point in your solution what if y is negative then the whole calculation will change.

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What is the units digit of 36^y?  [#permalink]

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New post Updated on: 07 Feb 2019, 23:40
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


Keyword: UD of \(6^(2y)\)

0 is neither +ive nor -ive, but is an even integer

y can take any value -ive integer, +ive integer.


(A) y is a positive integer
Sufficient

(B) y is an even integer
Can take 0, -ive and +ive values
Not sufficient

A
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Re: What is the units digit of 36^y?  [#permalink]

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New post 07 Feb 2019, 23:30
Basically the question is trying to test if one knows the fact that 0 is an even number.
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Re: What is the units digit of 36^y?  [#permalink]

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New post 09 Feb 2019, 04:13
Bunuel wrote:
What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer


Units digit of 36^y will be the same as the units digit of 6^y

St 1 : 6^(positive integer) will always end in 6

Sufficient

St 2 : 6^0 =1 units digit =1

6^2 = 36 units digit = 6

Not Sufficient

Choice A

Note : In St 2, We can also consider 6^(-2) which results in a decimal
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Re: What is the units digit of 36^y?   [#permalink] 09 Feb 2019, 04:13
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