Question

i am a 7 - digit number, my median is 5, my second and third digits are consecutive odd integers whose sum is 8. my first digit is 1 less than the sum of my second and third digits. the sum of my first and last digits is 9, my sixth digit is 3 more than my last digit and my fifth digit is 4 less than my median. who am i? write the answer in standard form.

Explanation:

Step1: Find second and third digits

Let the second digit be $x$ and third digit be $y$. Since they are consecutive odd integers and $x + y=8$, the only pair of consecutive odd - integers that sum to 8 is 3 and 5. So the second digit is 3 and the third digit is 5.

Step2: Find the first digit

The first digit is 1 less than the sum of the second and third digits. The sum of the second and third digits is $3 + 5=8$, so the first digit is $8 - 1=7$.

Step3: Find the last digit

The sum of the first and last digits is 9. Since the first digit is 7, the last digit is $9 - 7 = 2$.

Step4: Find the sixth digit

The sixth digit is 3 more than the last digit. Since the last digit is 2, the sixth digit is $2+3 = 5$.

Step5: Find the fifth digit

The fifth digit is 4 less than the median. Since the median (the fourth digit of a 7 - digit number) is 5, the fifth digit is $5 - 4=1$.

Step6: Form the 7 - digit number

The 7 - digit number is 7351152.

Answer:

7351152