Solving the Letter Cluster Analogy: ORANGE, MANGO, APPLE

This question asks us to find the relationship between pairs of letter clusters and apply the same relationship to a third word to find the missing cluster. We are given two pairs: ORANGE is related to FIQEWU, and MANGO is related to PIQER. We need to find the letter cluster related to APPLE in the same way.

Analyzing the Letter Cluster Pattern (ORANGE to FIQEWU)

Let's look at the first pair: ORANGE and FIQEWU. Both clusters have 6 letters. Let's try to find a rule that transforms ORANGE into FIQEWU.

Sometimes, the pattern involves reversing the word. Let's reverse ORANGE, which gives us EGNARO.

Now, let's compare the letters of the reversed word (EGNARO) with the letters of the target cluster (FIQEWU) based on their position in the alphabet (A=1, B=2, ...):

• E (5) $\rightarrow$ F (6): This is a difference of $+1$ (5 + 1 = 6).
• G (7) $\rightarrow$ I (9): This is a difference of $+2$ (7 + 2 = 9).
• N (14) $\rightarrow$ Q (17): This is a difference of $+3$ (14 + 3 = 17).
• A (1) $\rightarrow$ E (5): This is a difference of $+4$ (1 + 4 = 5).
• R (18) $\rightarrow$ W (23): This is a difference of $+5$ (18 + 5 = 23).
• O (15) $\rightarrow$ U (21): This is a difference of $+6$ (15 + 6 = 21).

The pattern seems to be: reverse the first word, and then add 1 to the alphabetical position of the first letter (of the reversed word), add 2 to the second, add 3 to the third, and so on, for each letter.

Verifying the Pattern (MANGO to PIQER)

Let's test this pattern with the second pair: MANGO and PIQER. MANGO has 5 letters.

Reverse MANGO: OGNAM.

Now, apply the same rule: add 1 to the first letter, 2 to the second, etc.

• O (15) + 1 = P (16)
• G (7) + 2 = I (9)
• N (14) + 3 = Q (17)
• A (1) + 4 = E (5)
• M (13) + 5 = R (18)

Putting these letters together gives us PIQER. This matches the second cluster in the given pair. So, the pattern holds true for both examples.

Applying the Pattern to APPLE

Now we apply the same rule to the word APPLE. APPLE has 5 letters.

Reverse APPLE: ELPPA.

Apply the addition rule sequentially:

• E (5) + 1 = F (6)
• L (12) + 2 = N (14)
• P (16) + 3 = S (19)
• P (16) + 4 = T (20)
• A (1) + 5 = F (6)

Combining the resulting letters, we get FNSTF.

Comparing with Options

Let's compare our result, FNSTF, with the given options:

• Option 1: ELPPA (This is just the reversed word)
• Option 2: GNSTG
• Option 3: FNSTF
• Option 4: ENSTE

Our calculated cluster FNSTF matches Option 3.

Revision Table: Letter Cluster Logic

Additional Information: Letter Coding Patterns

Letter cluster analogies and coding are common types of verbal reasoning questions. They test your ability to identify patterns based on the position of letters in the alphabet. Common patterns include:

• Simple Shift: Each letter is shifted by a fixed number of positions forward or backward (e.g., A $\rightarrow$ C, B $\rightarrow$ D is a +2 shift).
• Mixed Shift: The shift amount changes for each letter (e.g., +1, -2, +3, -4...).
• Reversal: The letters in the word are reversed.
• Positional Change: Letters are rearranged based on their position (e.g., 1st letter becomes last, 2nd becomes second last).
• Opposite Letters: Letters are replaced by their opposite letter in the alphabet (A is opposite Z, B is opposite Y, etc.).
• Combination of Rules: The pattern might involve reversing the word and then applying a shift, or applying a shift and then rearranging letters, like the pattern found in this question.

Solving these types of questions requires careful observation, knowledge of alphabetical order, and systematic testing of potential rules.