If 1<=x<=100, what fraction of values for integer x have the same unit

So all the number x between 1 & 100 inclusive, have the unit digit, between 0 & 9.

0^3 has unit digit 0 (qualified). So (10,20,30...100) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

1^3 has unit digit 1 (qualified). So (1,11,21,31...91) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

2^3 has unit digit 8 (not qualified).

3^3 has unit digit 7 (not qualified)

4^3 has unit digit 4 (qualified). So (4, 14,24,34...94) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

5^3 has unit digit 5 (qualified). So (5,15,25,35...95) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

6^3 has unit digit 6 (qualified). So (6,16,26,36...96) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

7^3 has unit digit 3 (not qualified).

8^3 has unit digit 2 (not qualified)

9^3 has unit digit 9 (qualified). So (9,19,29,39...99) 10 numbers satisfies the condition x's unit digit is same as x^3's unit digit.

=> There are 6 numbers for every 10 numbers between 1 and 100 (inclusive) that qualifies with the condition.

That is 6/10. So the answer is 3/5.

Hence the correct choice is E

Yes. Because 'X' can be 10, 20, 30 etc whose units digit is '0'.

Not digit 0, but all other integers ending with 0, viz 10,20,30,40,50,60,70,80,90 and 100.

integer values which result in same unit digit raised to power of 3
1,4,5,6,9,10
total such integers will be ( 1,4,5,6,9 ) would be 50 and for 10 would be 10
total 60
total integers 100
P = 60/100 ; 3/5
option E