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22 Sep 2011, 16:42
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Ans C:
Question asks for the units digit of 4 Power w = n,
1) w is even
2) w > 0
1) for all even values of w the units digit is 6, for example 4 p2 = 16, 4p4=16*16 , 4*6=16*16*16 like wise... however, w could be a positive even number or a negative even number. If w is negative, then units digit value varies and is not same for all negative even digits.
So A is eliminated.
2) For w > 0, unit digit of n can be 4 for w=1, and 6 for w=2 and so on. B alone is not possible.
3) If 1 and 2 are considered together, then for all positive even values of w the unit digit is always 6.
Ans : C. (Both 1 and 2 together).
Thank you.
Question asks for the units digit of 4 Power w = n,
1) w is even
2) w > 0
1) for all even values of w the units digit is 6, for example 4 p2 = 16, 4p4=16*16 , 4*6=16*16*16 like wise... however, w could be a positive even number or a negative even number. If w is negative, then units digit value varies and is not same for all negative even digits.
So A is eliminated.
2) For w > 0, unit digit of n can be 4 for w=1, and 6 for w=2 and so on. B alone is not possible.
3) If 1 and 2 are considered together, then for all positive even values of w the unit digit is always 6.
Ans : C. (Both 1 and 2 together).
Thank you.
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22 Sep 2011, 17:20
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The Answer is C.
Statement 1:
From this statement w is an even integer. So the value of w can be 0,2,4,6,8.... (remember : 0 is en even integer)
Case 1: When w = non zero even integers, the units digit of n is always 6. Lets try this by putting numbers:
4^2 = 16
4^4 = 256
4^6 = 4096....
We actually don't need to perform full multiplications. We can estimate the last digit by observing that every 4^2 has a units digit of 6 and 6 multiplied by 6 again yields a units digit of 6.
Case 2: When w=0, then 4^0 = 1 (concept used: any number raised to the power zero is 1)
from statement 1, we don't get a unique solution. Hence INSUFFICIENT.
Statement 2:
Since w>0, the values of w can be integer (odd and even) and fractions. So we can not get unique values as unit digit. Lets see this with example:
When w = 1/2, then 4^1/2 = 2 (units digit = 2)
When w=2, then 4^2 = 16 (units digit = 6)
When w = 1, then 4^1 = 4 (units digit = 4)
We don't get a unique solution. Hence INSUFFICIENT.
Combining A & B:
The value of w is even integer greater than 0, i.e. w= 2,4,6,8....
As explained in statement 1 above, the units digit of 4^w for all even integers except 0 will be 6.
Hence SUFFICIENT.
Statement 1:
From this statement w is an even integer. So the value of w can be 0,2,4,6,8.... (remember : 0 is en even integer)
Case 1: When w = non zero even integers, the units digit of n is always 6. Lets try this by putting numbers:
4^2 = 16
4^4 = 256
4^6 = 4096....
We actually don't need to perform full multiplications. We can estimate the last digit by observing that every 4^2 has a units digit of 6 and 6 multiplied by 6 again yields a units digit of 6.
Case 2: When w=0, then 4^0 = 1 (concept used: any number raised to the power zero is 1)
from statement 1, we don't get a unique solution. Hence INSUFFICIENT.
Statement 2:
Since w>0, the values of w can be integer (odd and even) and fractions. So we can not get unique values as unit digit. Lets see this with example:
When w = 1/2, then 4^1/2 = 2 (units digit = 2)
When w=2, then 4^2 = 16 (units digit = 6)
When w = 1, then 4^1 = 4 (units digit = 4)
We don't get a unique solution. Hence INSUFFICIENT.
Combining A & B:
The value of w is even integer greater than 0, i.e. w= 2,4,6,8....
As explained in statement 1 above, the units digit of 4^w for all even integers except 0 will be 6.
Hence SUFFICIENT.
22 Sep 2011, 17:29
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As the questions says 4 to the power w = n ,
The 1st statement is insufficient to answer the question because the units digit will always be a 6 when the power of 4 is even and not a zero. w=0,2,4,6,8....
The 2nd statement says the w is greater than zero , this is also insufficient as the units digits dont remain same for all powers of w. w=1,2,3,4,5,.....
Hence with combining both the statements the units digit is always 6 when the power w is greater than zero and even.
w=2,4,6,8....
ANswer is C
The 1st statement is insufficient to answer the question because the units digit will always be a 6 when the power of 4 is even and not a zero. w=0,2,4,6,8....
The 2nd statement says the w is greater than zero , this is also insufficient as the units digits dont remain same for all powers of w. w=1,2,3,4,5,.....
Hence with combining both the statements the units digit is always 6 when the power w is greater than zero and even.
w=2,4,6,8....
ANswer is C
