a number rounds off to 4000. the digit in the hundreds place is twice the digit in the tens place. the sum of the digits is 12. find the number uses only two different digits. find the number.

Answer 1

3500 <= n <= 4499
Let n = abcd
If a=4, b+c+d=12 and h=2d
Assuming c is not zero, c=4, since b≠c
But 4848 is no good

If a=3, c=3, so n = 3633

Note that if c=0, 4008 works as well

Answer 2

4800

Answer 3

Let n=wxyz
wxyz <= 4000
w= 3 (choose the closest possible number to be rounded off to 4)
x=2y
1<=y<=4 (because x value should not have 2 digits i.e. x=2(5)= 10)
w+x+y+z= 12
3+2y+y+z=12
3y+z= 9

*assume y=4
3(4)+z= 9
z= -3 : NOT POSSIBLE

*assume y=3
3(3)+z=9
z=0 : POSSIBLE

*assume y=2
3(2)+z=9
z=3; BUT, x=2y= 2(2)=4, hence you cannot round it off to a thousand
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w=3
x=2(3)= 6
y=3
z=0
w+x+y+z=12
3+6+3+0=12
3630<= 4000

Therefore, the number is 3630.