High School Math

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Sunday, April 03, 2005

Special Number

Tom has a very special four digit number.
To divide it by 7, you only had to drop its second digit.
What is the number?

An acceptable solution might be :
Let first digit be x,
second digit be y,
and third and fourth digits be z.
The number is 1000x + 100y +z.
Dropping the second digit gives value as 100x + z.
So, 1000x + 100y + z = 7(100x + z).
Or, 150x + 50y = 3z.
Since 50 is common on the left, and z is 2 digits, let z=50.
Then 3x + y = 3.
Since x is not zero, let us assume x=1, then y=0.
So the number is 1050.

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