Number Plate
Number Theory
Level
2
One Car Has 4 Digit Number Plate...
4th digit was double Of 1st Digit...
2nd and 3rd Digit Are Same...
And Last Two Digits Are Double Of First Two Digit...
What Is The Number Of Car Plate???...
The answer is 4998.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The numberplate can be represented as abcd.
d=2a
b=c
Now, it is abb(2a).
Since the two last digits are the double of the two first, we get this:
10a+b=1/2×(10b+2a)
10a+b=5b+a
9a=4b
This means that b has to be divisible by 9 and a has to be divisible by 4.
Since they both can only be one digit, b has to be 9, and by consequence a has to be 4.
Conclusion: the numberplate is 4998.