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12 Jul 2019, 04:31
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C
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Difficulty:
65%
(hard)
Question Stats:
52% (01:30) correct
48%
(01:30)
wrong
based on 176
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If x is a positive integer, what is the digit at the units place in the expansion of x^40?
(1) x is even
(2) x is not a multiple of five
(1) x is even
(2) x is not a multiple of five
12 Jul 2019, 04:32
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12 Jul 2019, 05:46
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raahulgupta12
P: x is a positive integer,
Q: What is the digit at the units place in the expansion of x^40?
#1: x is even
=> Last digit of x =0,2,4,6, or 8
Each of the digits 2^4k,4^4k,6^4k or 8^4k has last digit = 6 except 0
NOT SUFFICIENT
#2 x is not a multiple of five
Last digit of x^40 can not be determined since x can have multiple values and correspondingly last digit of x^40 can also have different values 1^40 =1 but last digit of 2^40 (1024^4) = 6
NOT SUFFICIENT
#1 & #2:
#1: x is even
#2 x is not a multiple of five
Then last digit of x =2,4,6,8 each x^4 will have last digit =6
=>last digit of x^40 =6
SUFFICIENT
IMO C
