Mystery Number! Clues are below!?

Question

Try to figure out the number.
It is : a 4 didgit whole number
divisible by 11,13,4,and 9
sum of digits is 12

Give me the correct answer and when I ask my teacher and she say it is right I will give you 5 points and the best answer.

tHE divisibility TEST FOR 4 IS THAT THE LAST 2 DIGITS OF THE NUMBER ARE DIVISBLE BY 4 LIKE THEY CAN BE DIVIDED IN 4.tHE DIVISIBILITY test FOR 9 IS WHEN YOU ADD ALL THE DIGITS THE NUMBER THAT COMES OUT IS DIVIDED EQUALLY INTO 9.

Answer 1

Not possible. None of those numbers have common factors, so at a minimum the number is a multiple of 4 * 9 * 11 * 13 = 5148.

Those digits add to 18, and if we multiply it by anything it will be bigger than 4 digits.

Another proof that it isn't possible is the fact that *every* number that is divisible by 9 has its digits adding up to a multiple of 9. 12 is *not* a multiple of 9 so you have conflicting requirements that can never be satisfied.

Either you have the multiples wrong, or you have the sum of digits wrong.

Perhaps your teacher just wants you to prove that no such number exists and the multiple of 9 test should do that.

Answer 2

Suppose that the mistake in the question is that the number is divisible by 3, not by 9. Then the sum of its digits is a multiple of 3, so 12 is possible.

The least common multiple of 3, 4, 11 and 13 is their product 1716. We can try 2, 3, 4 or 5 times this and still be within 4 digits. It turns out that only 2 times 1716 gives a number whose sum of digits is 12. I think that is the intended answer.

Answer 3

The sum of the digits is 18, not 12, for all numbers otherwise as specified.

11x13x4x9= 5148 (11x9=99, 100x4= 400, so 99x4=396; 400 x 13 = 5200, so 396 x 13 = 5148). Sum of digits = 5+1+4+8=18

All the divisors are relatively prime, so 5148 is the smallest number that meets the initial criteria, and doubling, which also meets the divisor criteria, makes the answer have 5 digits, not 4 (and the sum of digits is still 18).

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As a result of your updates and additions, the sum of the digits is not 12 as you originally stated, but must be 9, 18, 27 or 36. 5148 meets all the other requirements and has a sum of digits of 18, as mentioned. 5148 must be the answer.

Answer 4

Let this number be x.
If x existed then x = 4*9*11*13*m where m is an integer.
That is x = 5148m
m cannot be 1 because then, x = 5148 does not satisfy the condition that the sum of its digit is 12.
If m is any integer bigger or equal to 2, then x is bigger or equal to 2*5148 = 10296 which is not a 4 digit number.
So, x does not exist !

Either your missing something in the hypothesis or you're asking a trick question. Whichever one it is, I don't know. But you got your answer above :-)

Answer 5

For it to be divisible by 11,13,4 and 9 it must include as factors 2,2,3,3,11 and 13. The product of these factors is 5148, but this doesn't work because the sum of its digits is 18. Multiplying by any other prime factor would give a number more than 4 digits, so there is no such number.

Answer 6

11 = 11
13 = 13
4 = 2 x 2
9 = 3 x 3

11 x 13 x 4 x 9 = 5148

Sum 5+1+4+8 = 18

But, this does not meet your "sum of digits is 12" condition.

However, the sum of the last two digits is 12.

Answer 7

first you will do the multiplication with the given nos.
11x13x4x9= 5148
the answer is divisible by the given nos. like 5148 divide to 11 is equal to 468, 5148 divide to 13 is equal to 396, 5148 divide to 4 is equal to 1287 and 5148 divide to 9 is eqal to 572
if you add the 4 digit whole nos which is 5148
so 5+1+4+8=18 which is divisible by 9
18 divide to 9 is equal to 2

Answer 8

Actually no such number exists for the digits of all numbers divisible by 9 sum to a multiple of 9.

Answer 9

Well , I found 5148 but the sum of numbers is 18 not 12 :-?

Answer 10

It can't be done