Problem solving

Question

a three digit number satisfies the following conditions: The digits are consecutive whole numbers in increasing order; the sum of each pair of digits is greater than 4 and less than 10: and the tens digit is an odd number. What is the. Humber

Answer 1

Let the number be abc  ( example 358 which is not the answer)

 

The digits are consecutive numbers, thus 

b=a+1

and c= b+1

 

so the number becomes (a), (a+1) ,(a+2) at ones , tens and hundreds positions respectively

 

Now the question says

 

Sum of each pair is grater than 4 but less than 10

a+a+1 is grater than 4 but less than 10`

a+1+a+2 is grater than 4 but less than 10

and a+1 is an odd number

solving gives a lies between 0.5 and 4.5

 

but being whole numbers a lies between 1 and 4

 

so the possible answers are 123 or 234  . 123 does not meet the condition as 2 at tens position is even and not odd number

So the only valid answer is 234 ( two hundred thirty four)

Answer 2

Let x=1st, then x+1=2nd digit and x+2=3rd digit

 

4 < x + (x+1) < 10   or   3/2 < x < 9/2  which implies 2 < x < 4  since x is a whole number or x=3, which does not work since the tens digit would be 4 which is not an odd number

 

4 < x + (x+2) < 10   or  1 < x < 4  which is not restrictive enough

 

4 < (x+1) + (x+2) < 10  or  1/2 < x < 7/2  which implies 1 < x < 3  since x is a whole number  or x = 2

 

so the number is 234