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What is the units digit of 36^y? (A) y is a positive

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by VJesus12 » Thu May 03, 2018 10:27 am

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Answers

A

B

C

D

E

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Difficulty—

What is the units digit of 36^y?

(A) y is a positive integer

(B) y is an even integer

The OA is the option A.

Why is A the answer? Shouldn't it be D? When we calculate 36^{2k} the units digit will be 6. Am I wrong?
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Source: — Data Sufficiency |
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by Vincen » Thu May 03, 2018 11:22 am
Hello vjesus12.

Let's take a look at the question.

To know the units digit of 36^y, we only have to see the units digit of 6^y.

(A) y is a positive integer

This implies that y>0 and in this case the units digit of 6^y will be always 6. Therefore, this statement is SUFFICIENT.

(B) y is an even integer

Here, if we consider y=0 and y=2 we will get:

6^0 = 1.
6^1 = 6.

Hence, there are two different values. NOT SUFFICIENT.

This is why the correct answer is the option A.
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by Brent@GMATPrepNow » Thu May 03, 2018 2:23 pm
VJesus12 wrote:What is the units digit of 36^y?

(1) y is a positive integer
(2) y is an even integer
Target question: What is the units digit of 36^y?

Statement 1: y is a positive integer
So, y = 1 or 2 or 3 or 4 or 5 or...
Notice that 36^1 = 36 (units digit = 6)
Notice that 36^2 = ---6 (units digit = 6)
Notice that 36^3 = ---6 (units digit = 6)
Notice that 36^4 = ---6 (units digit = 6)
.
.
.
etc.
As we can see, if y is a positive integer, the units digit of 36^y MUST be 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y is an even integer
There are several values of y that satisfy statement 2. Here are two:
Case a: y = 0, in which case 36^y = 36^0 = 1. In this case, the units digit is 1
Case b: y = 2, in which case 36^y = 36^2 = ---6. In this case, the units digit is 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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