The digits of a three digit number are consecutive odd numbers. The number is 51 less than 30 times the sum of its digits. What is the number?

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9,7,5

5,7,9

7,5,9

5,9,7

answer is B.

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Detailed Solution

Concept- Start by assuming the number is the variable xyz According to your question, there are two possible cases. Either x is the largest or z is the largest. Solve both cases separately, construct the equations using the conditions given in the problem, and solve them to find the possible values of x, y, z and hence the number.
The required 3 digit number is xyz
Now, according to your question, x, y, and z are consecutive odd numbers. So there are two possible cases, depending on whether x is the maximum or z is the maximum.
Case 1 – If x is the largest, then

and

because there are consecutive odd numbers. Moreover, given that the number 51 is less than 30 times the sum of its digits. The number xyz is written as

.
So from this we know:

Plugging in the y and z values, we get:

Further solving for x gives:

However, since x is a number, its value cannot be negative or decimal. So this case is not possible. Case 1 - If z is the largest, then

and

because there are consecutive odd numbers. Moreover, given that the number 51 is less than 30 times the sum of its digits.
The number xyz
is written as

. So from this we know:

Plugging in the y and z values, we get:

Further solving for x gives:
Question Image

So the required value of x is 5 and

Hence, the correct answer is option (2) .

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