Given that the unit digits of A3and A are the same where A is a single digit natural number. How many possibilities can A assume ?

Open in App

Solution

$A^{3} = A 1^{3} = 1 2^{3} = 8 3^{3} = 27 4^{3} = 64 5^{3} = 125 6^{3} = 216 7^{3} = 343 8^{3} = 512 9^{3} = 729 It can be seen that, for values of A = 1, 4, 5, 6 and 9, A^{3} = A . So, A can assume 5 possibilities .$

Suggest Corrections

Similar questions

Q. If

x

and

y

are the number of possibilities that

A

can assume such that the unit digit of A and

A^{3}

are same and the unit digit of

A^{2}

and

A^{3}

are same respectively ,then the value of

x - y

is (where

A

is a single digit number)

Q. Product of the distinct digits of a natural number is 60. How many such numbers are possible?

N is a five-digit number such that all its digits are non-zero and even, and there is only a single repetition. If the repeated digits are adjacent, and N is divisible by 4, how many possible values can N take?

Q. 135 is a natural number whose "digit product" is

1 \times 3 \times 5 = 15

. How many such three digit numbers are possible with digit product 24?

Q. How many digits are possible in the square of a 'n' digit number?

Join BYJU'S Learning Program

Given that the unit digits of A3and A are the same where A is a single digit natural number. How many possibilities can A assume ?

A3=A13=123=833=2743=6453=12563=21673=34383=51293=729It can be seen that , for values of A=1 , 4 , 5 , 6 and 9 , A3=A .So, A can assume 5 possibilities.

$A^{3} = A 1^{3} = 1 2^{3} = 8 3^{3} = 27 4^{3} = 64 5^{3} = 125 6^{3} = 216 7^{3} = 343 8^{3} = 512 9^{3} = 729 It can be seen that, for values of A = 1, 4, 5, 6 and 9, A^{3} = A . So, A can assume 5 possibilities .$