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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What is the units digit of 36^y? (A) y is a positive
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Vincen
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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.
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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Brent@GMATPrepNow
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Your Answer
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B
C
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Target question: What is the units digit of 36^y?VJesus12 wrote:What is the units digit of 36^y?
(1) y is a positive integer
(2) y is an even integer
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
