Easy question for you?

Question

Find the smallest natural number n which has the following properties:

a) Its decimal representation has six as the last digit.
b) If the last digit 6 is erased and placed in the front of the remaining digits, the resulting number is 4 times as large as the original number n.

Answer 1

I will use the following:
n= your number; n= .....6
x= the number you obtain in case b; x= 4*n = 6.....
and I will wright the beginning and the ending of them, till I will get the final digit of the beginning to be the same as the first digit of the ending

Think about what happens if you try to multiply a number that has the last digit 6 with four,or if you try to divide a number that begins with 6 to 4.....

n= 1....6
x= 61....4

n= 15....46
x= 615....84

n=153....846
x= 6153.....384

so x=615384.......and n=153846

Let's check if x= 4*n
153846 *4 = 615384.......so it's correct

Answer 2

1

Answer 3

Let a be the number formed by every digit except the last. Then n=10a+6 and 4n=6*10^d+a, where d is the number of digits in a. This gives us the equation 6*10^d+a=4(10a+6). Solving for a, we get 6*10^d+a=40a+24 → 39a = 6*10^d-24 → a=(6*10^d-24)/39. All that remains is to try natural values of d until we get a natural number. Thus:

d=1, a=12/13
d=2, a=192/13
d=3, a=1992/13
d=4, a=19992/13
d=5, a=15384

Thus n=153846, and 4n=615384, as required.

Answer 4

Let A represent the 5-digit string (other than the 6).

The original number is 10A + 6, and
the new number is 600000 + A.

4(10A + 6) = 600000 + A
40A + 24 = 600000 + A
39A = 599976
A = 599976 / 39 = 15384

The original number is 153846.

Answer 5

X = 6 * 10 ^0 + A1*10^1 + ..... + An*10^n

4X = A1*10^0 + A2*10^1 + ... An*10^n-1 + 6*10^n

A1 = 0,2,4 because 4X is divisible by 4.

6 + A1 = 0 or 5 because 5X is divisible by 5.
thus A1 = 4
chechk the numbers 46,64 for the required properties

repeat this process until the correct number is found.

Answer 6

7

Answer 7

666

Answer 8

as u represented it as decimal then it cannot be natural number.. it will be real number i think

Answer 9

is this an easy answer

sorry cant do that im in a hurry

Answer 10

This reminds me of this one time at band camp.. yuo can take it from there