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23 Sep 2011, 10:56
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The correct ans is C.
1. w is even integer implies it can be 0,2,4,6,8...
in all cases units digit of 4^w is 6 except when w=0, when the units digit is 1.
2. When w>0, units digit will be 4 when w is odd and 6 when w is even.
3. when you combine the two statements w will be an even integer other than 0. Hence, the units digit of 4^w will always be 6
1. w is even integer implies it can be 0,2,4,6,8...
in all cases units digit of 4^w is 6 except when w=0, when the units digit is 1.
2. When w>0, units digit will be 4 when w is odd and 6 when w is even.
3. when you combine the two statements w will be an even integer other than 0. Hence, the units digit of 4^w will always be 6
23 Sep 2011, 11:11
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The answer is C - Both options together are sufficient.
4^w = n So, the units digit of n can be either 1, 4 or 6 depending on whether w is 0, odd or even.
i.e. if w is 0 then 4 ^ 0 = 1 = n, so units digit of n is 1
if w is odd i.e. 1, 3, 5, etc then 4 ^ (odd integer) = number with units digit 4
if w is even i.e. 2, 4, 6, etc then 4 ^ (even integer) = number with units digit 6
Given,
1. w is an even integer --> Not sufficient
if w is 0 which is even, units digit of 4 ^ w will be 1 and if w is an even integer other than 0, units digit of 4 ^ w will be 6
2. w > 0 --> Not sufficient
if w is odd, units digit of 4 ^ w will be 4 and if w is even, units digit of 4 ^ w will be 6
Taking 1 and 2 together, if w is an even integer and if w is greater than 0, the possible options for w are 2, 4, 6, etc. In all such cases, 4 ^ w will always be a number with units digit 6 - hence sufficient.
4^w = n So, the units digit of n can be either 1, 4 or 6 depending on whether w is 0, odd or even.
i.e. if w is 0 then 4 ^ 0 = 1 = n, so units digit of n is 1
if w is odd i.e. 1, 3, 5, etc then 4 ^ (odd integer) = number with units digit 4
if w is even i.e. 2, 4, 6, etc then 4 ^ (even integer) = number with units digit 6
Given,
1. w is an even integer --> Not sufficient
if w is 0 which is even, units digit of 4 ^ w will be 1 and if w is an even integer other than 0, units digit of 4 ^ w will be 6
2. w > 0 --> Not sufficient
if w is odd, units digit of 4 ^ w will be 4 and if w is even, units digit of 4 ^ w will be 6
Taking 1 and 2 together, if w is an even integer and if w is greater than 0, the possible options for w are 2, 4, 6, etc. In all such cases, 4 ^ w will always be a number with units digit 6 - hence sufficient.
