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
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.
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.
i cant find out what the range is for normal numbers e.g 6 4 8 67 2 3 9 5
To solve this question, we need to carefully analyze the information given and use logical reasoning.
Let's break down the information:
1. The sum of the digits of a three-digit number is 12.
2. The hundreds digit is 3 times the tens digit.
3. The tens digit is 1/2 the units digit.
First, let's represent the digits of the number as variables. Let's call the hundreds digit H, the tens digit T, and the units digit U.
We can form an equation based on the first statement:
H + T + U = 12
Now, let's use the second and third statements to form additional equations:
H = 3T (hundreds digit is 3 times the tens digit)
T = 1/2U (tens digit is 1/2 the units digit)
We now have a system of three equations that we can solve to find the values of H, T, and U.
Substituting the value of H from equation 2 into equation 1, we get:
3T + T + U = 12
4T + U = 12
Now, let's substitute the value of T from equation 3 into this equation:
4(1/2U) + U = 12
2U + U = 12
3U = 12
U = 4
We have found that the units digit (U) is 4. Now, let's find the value of T:
T = 1/2U
T = 1/2(4)
T = 2
Therefore, the tens digit of the number is 2.
The correct answer is 2 (according to one of the provided answer choices).