The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

1. 21
2. 25
3. 41
4. 67

Let the four 2-digit odd numbers be: n-3, n-1, n+1, n+3

Sum of these 4 numbers = 4n

When the sum is divided by 10, you get a perfect square that include 1, 4, 9, 16, 25, 36, 49, and so on.

Possible values of 4n/10 are 4, 16, 36, ...

If 4n/10 = 4, then n = 10; The corresponding numbers are 7, 9, 11, 13 (all of which are 2-digit)

If 4n/10 = 16, then n = 40; The corresponding numbers are 37, 39, 41, 43

If 4n/10 = 36. then n = 90; The corresponding numbers are 87, 89, 91, 93

The correct option is C.
The passage presents a mathematical problem involving four consecutive two-digit odd numbers and their sum, which when divided by 10, results in a perfect square. It then provides a solution to identify one of these numbers from a list of options.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

1. 21
2. 25
3. 41
4. 67

Let the four 2-digit odd numbers be: n-3, n-1, n+1, n+3

Sum of these 4 numbers = 4n

When the sum is divided by 10, you get a perfect square that include 1, 4, 9, 16, 25, 36, 49, and so on.

Possible values of 4n/10 are 4, 16, 36, ...

If 4n/10 = 4, then n = 10; The corresponding numbers are 7, 9, 11, 13 (all of which are 2-digit)

If 4n/10 = 16, then n = 40; The corresponding numbers are 37, 39, 41, 43

If 4n/10 = 36. then n = 90; The corresponding numbers are 87, 89, 91, 93

The correct option is C.
user
The passage presents a mathematical problem involving four consecutive two-digit odd numbers and their sum, which when divided by 10, results in a perfect square. It then provides a solution to identify one of these numbers from a list of options.

TYPE: SINGLE_QUESTION_WITH_ANSWER