Four Digits
Find a Four Digit Number, whose-
- Second and Third digits are equal.
- Fourth digit is twice the first digit, and
- 1st and 2nd digits combined is half of 3rd and 4th digits combined.
For example, if the number is x y y z , then we have 2 × x = z and 2 × x y = y z .
Note: x y is equal to 1 0 x + y . It is not equal to x × y .
The answer is 4998.
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2 solutions
why not 2334
I think the word "combine" means addition? i don't think it says a product?
why not 1224 and 2448?
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2 times 2=/=8 and 1 times 2=/=4, the problem says z=2 x,not 4 x
Look at the equations. It does not say 2 × x × y = y × z . The line above it indicates that it is to be read as a number, instead of a multiplication. IE x y = 1 0 x + y .
Please post only those questions that have a unique solution.
In accordance with the given conditions we have z=2x and also 2 xy=yz, its can be simpliflied using place values to (10 x+1 y) 2=(10 y+2 x) Which further gets reduces to 18x=8y or 9x=4y specifically! This expression has satisifactory solution at numeric values of x=4 and y=9. Hence the 4'digit number is xyyz=4998.
How about 1222
Why not 1002 or 2004 or 3006 or 4008 .... they all satisfy the needs ... huh!
what about 3446?
Let the number be x y y z (first equation).
The second equation tells us that z = 2 x .
The third equation tells us that 2 ( 1 0 x + y ) = 1 0 y + z . Hence, this gives us 9 x = 4 y .
Since x and y are non-zero digits from 1 to 9, the only possible solution is x = 4 and y = 9 .
Hence, this gives us 4 9 9 8 .