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hongwang9703
- Senior | Next Rank: 100 Posts
- Posts: 73
- Joined: Wed Jul 22, 2009 6:46 pm
- Location: Buffalo
If y is divisible by the square of an even prime number and x is the actual square of an even prime number, then what is the units digit of xy?
0,2,4,6,8 are the answer choices
First, let's identify the value of the square of the only even prime number. The only even prime is 2, so the square of that is 22 = 4. Thus, x = 4 and y is divisible by 4. With this information, we know we will be raising 4 to some power divisible by 4. The next step is to see if we can establish a pattern.
41 = 4
42 = 16
43 = 64
44 = 256
45 = 1024
We will quickly notice that 4 raised to any odd power has a units digit of 4. And 4 raised to any even number has a units digit of 6. Therefore, because we are raising 4 to a number divisible by 4, which will be an even number, we know that the units digit of xy is 6.
The correct answer is D.
but y could also be 1, which will cause the digit number toi be 4...right?
0,2,4,6,8 are the answer choices
First, let's identify the value of the square of the only even prime number. The only even prime is 2, so the square of that is 22 = 4. Thus, x = 4 and y is divisible by 4. With this information, we know we will be raising 4 to some power divisible by 4. The next step is to see if we can establish a pattern.
41 = 4
42 = 16
43 = 64
44 = 256
45 = 1024
We will quickly notice that 4 raised to any odd power has a units digit of 4. And 4 raised to any even number has a units digit of 6. Therefore, because we are raising 4 to a number divisible by 4, which will be an even number, we know that the units digit of xy is 6.
The correct answer is D.
but y could also be 1, which will cause the digit number toi be 4...right?
i got utterly defeated by the gmat.
