What is the number?

Question

the thousands digit of a 4 digit numberis 4 greater that the hundreds digit. the ten digit is 2 times the thousands digit and the ones digit is 1/2 the thousands digit...What is the number?

Answer 1

Jeremy is right, but he doesn't explain how he got there.

Let the number be ABCD.

We have the following facts:

1) A = B + 4
2) B = A - 4
3) C = 2 A
4) D = A / 2

From #4, 2 D = A. So in #3, C = 2 (2 D) = 4 D.

This gives us an important clue. Since C = 4 D, C / D = 4 / 1, which means C is either 4 or 8 and D is either 1 or 2. Let's test D = 1. If D = 1, then A = 2 from equation #4. If we put A = 2 into #1, then B = 2 - 4 = -2, which is an impossibility. So, D cannot be equal to 1. That leads us to conclude D = 2. That forces us to conclude also that C = 8, since C = 4 D.

Now we are getting somewhere, because if C = 8, from #3, A = 4, and we have fixed values for three of our letters which we can test.

Let A = 4. Then from #1, A = B + 4 implies B = 4 - 4 = 0.

Now we are ready to check out all of our calculated values to see if they work.

1) 4 = 0 + 4
2) 0 = B
3) 8 = 2 (4)
4) 2 = 4 / 2

So, the number must be 4082.

Answer 2

This is a logic question in disguise...

let y be the thousands digit. By the description,
y-4 is the hundreds digit,
2y is the tens digit, and
1/2 y is the ones digit

You know that for all of the place holders that the number is from 0 to 9 (thousands, hundreds, tens, ones).

Because of that you know that the number y cannot be greater than 4 (because in the tens digit, y > 5 is greater than 9).

You also know that the each of the place holders the number has to be greater than or equal to 4 (because in the hundreds digit a number less than 4 would result in a negative number).

Because of that you know that the number must be 4. So the number you are looking for is:

4082

Answer 3

The thousands digit has to be even (8, 6, 4, 2). But the tens digit is twice the thousands digit. Thus it can't be 8 or 6. Finally, the hundreds digit is 4 less than it... so it can't be 2. That leaves 4.

From there you have:
4082

Answer 4

assume the number is abcd
so we have
a = 4+b
c=2*a
d= 1/2 *a
and all a, b, c, d are digits of (0,1,2,3,4,5,6,7,8,9) and a can not be 0

from c=2*a, we have a can only be 1,2,3,4 and c can only be 2,4,6,8, respectively,
from d = 1/2 * a, we know a can not be 1
so a can only be 2,3,4

as a=b+4 and the minimum value for b is 0, so the minimum value for a is 4.. so a can not be 2, and 3.

so a =4
b=0
c =8
and d =2

the number is 4082

Answer 5

This can be solved easily enough by a bit of algebra, remembering the constraint that no digit can exceed 9.

Answer 6

The number is 4082.

Answer 7

4082 or something like that but dont ask me ask your math teacher and if they cant help then put a random answer in it

Answer 8

4082 works

Answer 9

4082

Answer 10

your answer is 4082