Posted by **Anonymous** on Tuesday, April 15, 2008 at 1:36pm.

This is an SAT Question of the Day. The sum of the digits of a three-digit 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

- math -
**Reiny**, Tuesday, April 15, 2008 at 1:55pm
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

- math -
**DrBob222**, Tuesday, April 15, 2008 at 2:03pm
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.

- math -
**Anonymous**, Tuesday, April 15, 2008 at 2:12pm
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.

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