Understanding the Letter-Number Series Pattern

The question asks us to complete a given series: $u_v_w_35 x_40 y_45 z_50$. This series contains a mix of letters and numbers, with several blanks (underscores) that need to be filled logically.

Analyzing the Letter Sequence

First, let's look at the letters present in the series:

• u
• v
• w
• x
• y
• z

These letters follow a simple alphabetical order. Each letter is the next one in the alphabet.

Analyzing the Number Sequence and Blanks

The series structure suggests an interleaved pattern. Let's identify the positions of the blanks and the given numbers:

$u _ v _ w _ 35 x _ 40 y _ 45 z _ 50$

There are 6 blanks to fill using the numbers provided in the options. The numbers already present are 35, 40, 45, and 50.

Identifying the Pattern Logic

Let's use the correct answer option, which provides the numbers: $20, 25, 30, 36, 41, 46$, to fill the blanks in the order they appear:

• The blank after 'u' is filled with 20.
• The blank after 'v' is filled with 25.
• The blank after 'w' is filled with 30.
• The blank after 'x' is filled with 36.
• The blank after 'y' is filled with 41.
• The blank after 'z' is filled with 46.

Substituting these numbers into the series gives us:

$u 20 v 25 w 30 35 x 36 40 y 41 45 z 46 50$

Now, let's examine the complete number sequence formed by combining the filled blanks and the original numbers:

$20, 25, 30, 35, 36, 40, 41, 45, 46, 50$

Let's find the difference between consecutive numbers in this sequence:

• $25 - 20 = 5$
• $30 - 25 = 5$
• $35 - 30 = 5$
• $36 - 35 = 1$
• $40 - 36 = 4$
• $41 - 40 = 1$
• $45 - 41 = 4$
• $46 - 45 = 1$
• $50 - 46 = 4$

The pattern observed in the number sequence is: three additions of 5, followed by a repeating pattern of adding 1 and then adding 4 (+5, +5, +5, +1, +4, +1, +4, +1, +4).

Completing the Series

The letters 'u', 'v', 'w', 'x', 'y', 'z' simply progress alphabetically. The numbers follow the identified pattern (+5, +5, +5, +1, +4, ...), filling the blanks logically.

Therefore, the set of numbers $20, 25, 30, 36, 41, 46$ correctly completes the given letter-number series.