math
posted by Anonymous .
This is an SAT Question of the Day. The sum of the digits of a threedigit number is 12. If the hundreds digit is 3 times the tens digit and the tens digit is 1 over 2 the units digit, what is the tens digit of the number?
The way the question is phrased is very confusing.
The answer choices are:
2
3
4
6
9

let the tens digit be x
then the hundreds digit is 3x and
the unit digit is 2x
then x + 3x + 2x = 12
x = 2
check: my number must be 624, all the stated conditions are met
so the correct answer is 2 
One easy way to solve this is to try the numbers given as choices.
If the number is XYZ, then X+Y+Z=12
We know X=3Y (hundreds digit(X) is 3*tens digit(Y) so X = 3Y.
We also know the tens digit (Y) is 1/2 the units digit(Z) so 1/2*Z = Y which I rearranged to Z = 2Y
Now make a table
X.....Y.....Z......Sum

6.... 2 ... 4 ..... 12 and the first try gets it. If Y = 2, then X = 3Y = 3*2 = 6. If Y=2, then Z = 2Y = 4
and 6+2+4=12. Voila!
You can quickly go through the others to see that they won't work.
If Y = 3, then X = 9 and Z can't be a number because we're already at 12.
If Y = 4, then X = 12 and we've exceeded 12.
If Y = any other whole number, then 3*Y exceeds 12. Therefore, the tens digit must be 2. The number is 624. Check my thinking. Check my work. 
i cant find out what the range is for normal numbers e.g 6 4 8 67 2 3 9 5

The explanation said:
If x stands for the tens digit, then 3x stands for the hundreds digit and 2x stands for the units digit. Since the sum of the digits is 12, 3x + x + 2x = 12. Solving this gives x = 2.
Thank you for your help.