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
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.
3 answers
4800
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
---
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.
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
---
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.