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Re: What is the digit at the unit's place in the expansion
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10 Apr 2018, 15:24
Statement 1 x is even > units digit of x can be 0,2,4,6,8 if units digit is 0, then x^40 has units digit 0 if units digit is 2, then x^40 has units digit 6 because 2 raised to a power that's a multiple of 4 has 6 as the units digit. if units digit is 4, then x^40 has units digit 6 because 4=2^2 > (2^2)^40=2^80 > 80 is a multiple of 4 if units digit is 6, then x^40 has units digit 6 if units digit is 8, then x^40 has units digit 6 because 8=2^3 > (2^3)^40=2^120 > 120 is a multiple of 4 So units digit of x^40 can be 0 or 6. Not sufficient
Statement 2 x is not a multiple of 5 > units digit of x can be 1,2,3,4,6,7,8,9 Not sufficient
Combining 1&2 Units digit of x can be 2,4,6,8, thus x^40 will have 6 as the units digit. Sufficient
Answer: C
