What is the units digit of 36^y?

Question

(A) y is a positive integer

(B) y is an even integer

HKD1710 · Accepted Answer

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

NandishSS · Answer

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

NandishSS · Answer

Ops I missed 0

Thanks for pointed out!!!

What if in (B)y is an even integer

Y=-2, is this valid?

ScottTargetTestPrep · Answer

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

awdxzs · Answer

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

Posted from my mobile device

KanishkM · Answer

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

gmataaj · Answer

Basically the question is trying to test if one knows the fact that 0 is an even number.

ksrutisagar · Answer

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

What is the units digit of 36^y?

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GMAT Data Sufficiency (DS) Questions

What is the units digit of 36^y?

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