A number arrangement machine takes an input line of five numbers and rearranges them through a series of steps according to a specific rule:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759767201/aptidude_questions/uzyzagohu4pmyv3nks4b.png)

Which of the following represents the **penultimate step** (Step IV) of the arrangement?

Question

A number arrangement machine takes an input line of five numbers and rearranges them through a series of steps according to a specific rule:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759767201/aptidude_questions/uzyzagohu4pmyv3nks4b.png)

Which of the following represents the **penultimate step** (Step IV) of the arrangement?

Accepted Answer

**Solution:**

1. **Step I:** For each number, multiply the 1st and 2nd digits, subtract 1 from the middle digit, then multiply the 4th and 5th digits. This produces the first transformed set.

2. **Step II:** Arrange the odd numbers in descending order followed by even numbers in descending order.

3. **Step III:** Remove the first digit of each number. Then, add the 2nd and 3rd digits and write the square of this sum. Similarly, add the 4th and 5th digits and write the square of this sum.

4. **Step IV (Penultimate Step):** Sum the 1st and 2nd numbers, 3rd and 4th numbers, and so forth, to get the next set.

5. **Step V:** Calculate the digit sum of each number, write the square of this digit sum, and then arrange the digit sum followed by its square.

For the input 28465 79784 63452 34867 93275, the penultimate step (Step IV) is:

$$128 \quad 106 \quad 122 \quad 90 \quad 117$$

**Answer:** Option (c) 128 106 122 90 117

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