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Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base. So, the last digit of \(66^6\) is 6 and the last digit of \(5^{55}\) is 5. Therefore, the answer would be xxxx6-xxxx5=1, B.
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Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base. So, the last digit of \(66^6\) is 6 and the last digit of \(5^{55}\) is 5. Therefore, the answer would be xxxx6-xxxx5=1, B.

Unit digit of 66^6 is 6 and 5^55 is 5 But we do not know which one is greater, so unit of difference can be 1 or 9 But from given data 66x66x66x66x66x66 or 66^6 <<< 125x125x125x125x125x125 x 5^37 or 5^55 Hence unit digit is 9 and answer is E

Re: What is the units digit of 66^6 - 5^55? [#permalink]

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14 Oct 2017, 21:42

Answer : 9 Answer : E

Obviously 66^6 will give a units digit of 6. and 5^55 will give a units digit of 5.

But 6-5 = 1 will only apply if there is no carrying forward meaning, that the "6" number is larger than the "5" Number.

Doing some math though tells us that the "5" number is indeed much larger, which means carrying forward does take place. Making the subtraction look much more like 15 - 6 = 9, than the aforementioned 6 - 5 = 1.