Select the option that is related to the third letter-cluster in the same way…

To solve this analogy, we need to identify the pattern used to transform the first word, BRANCH, into the second word, ARBHCN, and then apply the same rule to BURDEN.

Step-by-Step Pattern Analysis
Analyze the transformation (BRANCH to ARBHCN):

Original word: B R A N C H (Positions: 1 2 3 4 5 6)

Transformed word: A R B H C N

Let's break this down by position:

The first two letters (B, R) are swapped to become (R, B). Wait, let's look closer: A R B H C N.

Actually, the pattern is:

Swap the first two letters: B R becomes R B? No, the word starts with A R.

Let's look at the letters:

A (Pos 3) moved to Pos 1

R (Pos 2) moved to Pos 2

B (Pos 1) moved to Pos 3

H (Pos 6) moved to Pos 4

C (Pos 5) moved to Pos 5

N (Pos 4) moved to Pos 6

The rule described in the solution is "swapping positions 1-2 and reversing the rest." Let's re-test that:

BRANCH

Swap 1 & 2: RBANCH

Reverse the rest (ANCH): H CNA

Result: RBHCNA. This does not match ARBHCN.

Let's look at the transformation again: B R A N C H -> A R B H C N

Letters 1, 2, 3 (B, R, A) become 3, 2, 1 (A, R, B). This is a reversal of the first three letters.

Letters 4, 5, 6 (N, C, H) become 6, 5, 4 (H, C, N). This is a reversal of the last three letters.

Applying the Rule (Reverse 1-3, Reverse 4-6) to BURDEN
Word: B U R D E N (Positions: 1 2 3 4 5 6)

Reverse first three (B U R): R U B

Reverse last three (D E N): N E D

Result: RUBNED