Math, asked by MKirthiga, 9 months ago

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 ?
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Answers

Answered by g4learner
16

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

Answered by Anonymous
71

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

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