Who am I ? 1) I am a 3 digit number. 2) I am a composite number. 3) The difference of my ones and hundreds digit is 6. 4) My ones digit is equal to the sum of hundreds and tens digit. Who am I ?
IRREVELANT ANSWER WILL BE REPORTED.
Answers
Answer:
Step-by-step exp
hundred's digit is 6 less than ones digit
so it leaves us with options
(hundred, ones digit) (3,9), (2,8),(1,7)
ones digit is the sum of tens and hundreds
3, x, 9 cant be possible bcz middle digit would be 2 with 10 carried over
(2, x, 8) ones digit is 8 , hundred is 2, hence 6 is the tens digit
268 is the number
Your Answer:
Let the number be (100x + 10y + z)
So, first case is fulfilled.
It is a composite number. More than two factors.
Now,
z - x = 6 -------->(1)
And
z = x + y ----------->(2)
So, from first equation we can conclude that
z = 6 + x ------------>(3)
from 2nd and 3rd equation we can conclude that
x + y = 6 + x
=> y = 6
from observing 1st Equation. We conclude that the possible numbers are
(ones,hundreds) = (9,3), (8,2), (7,1)
Now we also know that the middle term is 6
So,
In first Case
Where ones digit is 9 and hundreds digit is 3
So, Adding tens digit and hundreds digit.
3 + 6 = 9, So, it is verifying the relationship of second Equation
Now, forming the number
So, we get 369
and it is also a composite number.
So, it is confirming all the requirements that the three digit number wants. So, it is a number we get
Now, Second Case
Where ones digit is 8 and hundreds digit is 2
So, Adding tens digit and hundreds digit.
2 + 6 = 8, So, it is verifying the relationship of second Equation
Now, forming the number
So, we get 268
and it is also a composite number.
So, it is confirming all the requirements that the three digit number wants. So, it is a number we get
Now, Third Case
Where ones digit is 7 and hundreds digit is 1
So, Adding tens digit and hundreds digit.
1 + 6 = 7, So, it is verifying the relationship of second Equation
Now, forming the number
So, we get 167
and it is not a composite number.
So, it is not confirming all the requirements that the three digit number wants. So, it is not a number we want.
So, the answer is 369, 268