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Sunday, May 3, 2009
Problem 17 - GMAT Powers & Roots
What is the value of x if x is the units digit of 3^23 - 3?
A more not so quick solution: 3 =3 3^2 =9 3^3 =27 3^4 =81 or 3^4= 81 or 3^4=1(mod 10) or 3^4k = 1 (mod10) 3^23 = 3^20.3^3 3^3=7(mod10) Multiplication of modulo: 3^23=7(mod10) or 3^23=(4+3)(mod10) 3^23-3=4(mod10) Remainder 4.
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Find mod 10
ReplyDelete3^4 = 1 (mod 10)
we are left with, 3^3 -3 = 24 = 4 (mod 10)
A more not so quick solution:
ReplyDelete3 =3
3^2 =9
3^3 =27
3^4 =81
or 3^4= 81 or 3^4=1(mod 10)
or 3^4k = 1 (mod10)
3^23 = 3^20.3^3
3^3=7(mod10)
Multiplication of modulo:
3^23=7(mod10) or
3^23=(4+3)(mod10)
3^23-3=4(mod10)
Remainder 4.
3^1=3 ; 3^2=9 ; 3^3=27 ; 3^4=81 ... so we have 1,9,7 and 1 repeating at unit's place.Check for 23th time i.e 7, so 7-3 =4 is the remainder.
ReplyDelete