Car and a weird nmber

A car's license plate consists of 4 digits in the following manner:

1) The last digit is twice that of first digit.
2) The second and third digits are the same.
3) Last two digits are twice that of the first two digits( for eg: if last two digits are 44, then the first two numbers are 22).

Identify the number of the car.


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.

4 solutions

Because the last two digits are the double of first two digits, its impossible for first digit is 5 or more since if its doubled must be more than 100 (more than 2 digits).
If the 1st digit is 1, the 3rd digit must be 2 or 3, but 1224 and 1332 aren't the answer.
If the 1st digit is 2, the 3rd digit must be 4 or 5, but 2448 and 2550 aren't the answer.
If the 1st digit is 3, the 3rd digit must be 6 or 7, but 3662 and 3774 aren't the answer.
If the 1st digit is 4, the 3rd digit must be 8 or 9. 4888 and 4998. Giving 4998 as the correct answer.
If the 1st digit is 0, the 3rd digit must be 0 or 1. 0110 isn't the answer. 0000 I don't know, I try 4998 and solved it.


0000 wasn't allowed

Aloysius Ng - 7 years ago
Roger Erisman
Mar 4, 2016

Consider the digits of the number as "abcd".

We know d = 2a.

b= c

10c + d = 2 (10a + b) = 20a + 2b { 2 digit numbers "xy" have a value of 2 x + y}

Substituting: 10c + d = 10(d) + 2(c)

Which gives: 8c = 9d

LCM of 8 and 9 is 72 which leads to c = 9 and d = 8

Using the given information a = 4 and b = 9

The number is 4998.

Why was 0000 wrong? It consists of 4 digits and all 3 criteria are met.

Suraj R. Gupta
Jun 1, 2014

4x2=8 99 49x2=98

4998

If numbers is of the form [x][y][y][2x], As last 2 digits are twice that of the first 2 digits Considering [x][y] & [y][2x] as separate two digit numbers 2(10x+y)= (10y+2x) ,9x=4y, for x=4, y=9 So number is 4998

Devendra Marghade - 6 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...