The question asks us to find the letter-cluster that is related to CALM in the same way that KRAV is related to PITY. This is a letter-cluster analogy problem where we need to identify the pattern or rule connecting the first pair of letter-clusters and apply it to the third letter-cluster to find the fourth one.

Analysing the Relationship between PITY and KRAV

Let's look at the letters in PITY and KRAV and their positions in the alphabet. We should try to find a rule that transforms PITY into KRAV.

• P is the 16th letter.
• I is the 9th letter.
• T is the 20th letter.
• Y is the 25th letter.

So, PITY corresponds to the positions 16, 9, 20, 25.

Now let's look at KRAV:

• K is the 11th letter.
• R is the 18th letter.
• A is the 1st letter.
• V is the 22nd letter.

KRAV corresponds to the positions 11, 18, 1, 22.

Let's try to see if there's a direct relationship between the letters at the same position:

• P(16) to K(11): $16 - 11 = 5$. Difference is -5.
• I(9) to R(18): $18 - 9 = 9$. Difference is +9.
• T(20) to A(1): $1 - 20 = -19$. Or, cyclically, $20 \to 21 \to ... \to 26 \to 1$, which is $+7$ steps ($20+7=27 \equiv 1 \pmod{26}$). Let's consider $+7$.
• Y(25) to V(22): $22 - 25 = -3$. Difference is -3.

The pattern seems to be -5, +9, +7, -3. Let's see if applying this to CALM works.

• C(3) - 5 = -2 (Cyclic: $3 - 5 = -2 \equiv 24 \pmod{26}$, which is X).
• A(1) + 9 = 10 (J).
• L(12) + 7 = 19 (S).
• M(13) - 3 = 10 (J).

This gives XJSJ, which is not among the options. So, the relationship is likely not a direct position-wise transformation.

Discovering the Reordering and Transformation Rule

Let's investigate if the letters in KRAV are derived from the letters in PITY but in a different order. Let's try applying a simple shift to the letters of PITY and see if they match the letters of KRAV when reordered. A common shift is +1, +2, etc.

Let's try adding 2 to each letter of PITY:

• P + 2 = R (16+2=18)
• I + 2 = K (9+2=11)
• T + 2 = V (20+2=22)
• Y + 2 = A (25+2=27 $\equiv$ 1, cyclically)

Applying +2 shift to PITY gives the letters R, K, V, A. These are exactly the letters in KRAV (K, R, A, V), just in a different order.

Let's see how the letters from PITY map to the letters in KRAV after the +2 shift:

• The 2nd letter of PITY (I) becomes K (I+2). K is the 1st letter of KRAV.
• The 1st letter of PITY (P) becomes R (P+2). R is the 2nd letter of KRAV.
• The 4th letter of PITY (Y) becomes A (Y+2). A is the 3rd letter of KRAV.
• The 3rd letter of PITY (T) becomes V (T+2). V is the 4th letter of KRAV.

So, the rule is: Apply a +2 shift to each letter of the first word, and then arrange the resulting letters in a specific order to form the second word. The order is derived as follows:

This table shows that:

• The 1st letter of KRAV comes from the 2nd letter of PITY (+2).
• The 2nd letter of KRAV comes from the 1st letter of PITY (+2).
• The 3rd letter of KRAV comes from the 4th letter of PITY (+2).
• The 4th letter of KRAV comes from the 3rd letter of PITY (+2).

Applying the Rule to CALM

Now, let's apply the same rule to CALM. CALM has 4 letters:

• 1st letter: C
• 2nd letter: A
• 3rd letter: L
• 4th letter: M

Let the resulting letter-cluster be W1 W2 W3 W4.

• W1 (1st letter of the result) is derived from the 2nd letter of CALM (+2). 2nd letter is A. A + 2 = C (1+2=3). So, W1 = C.
• W2 (2nd letter of the result) is derived from the 1st letter of CALM (+2). 1st letter is C. C + 2 = E (3+2=5). So, W2 = E.
• W3 (3rd letter of the result) is derived from the 4th letter of CALM (+2). 4th letter is M. M + 2 = O (13+2=15). So, W3 = O.
• W4 (4th letter of the result) is derived from the 3rd letter of CALM (+2). 3rd letter is L. L + 2 = N (12+2=14). So, W4 = N.

Combining the letters W1, W2, W3, W4, we get CEON.

Therefore, CALM is related to CEON in the same way that PITY is related to KRAV.

Checking the Options

Let's compare our result CEON with the given options:

1. CEON
2. CENO
3. ECNO
4. ECON

Our calculated result CEON matches option 1.

Final Answer Derivation

The relationship between PITY and KRAV involves adding 2 to the alphabetical position of each letter in PITY and then rearranging them to form KRAV. Specifically, the letters of PITY at positions 2, 1, 4, 3 (I, P, Y, T) become the letters of KRAV at positions 1, 2, 3, 4 (K, R, A, V) respectively, after adding 2 to their positions.

Applying this rule to CALM (letters at positions 1, 2, 3, 4 are C, A, L, M):

• Letter at new position 1 = (Letter at CALM position 2) + 2 = A + 2 = C
• Letter at new position 2 = (Letter at CALM position 1) + 2 = C + 2 = E
• Letter at new position 3 = (Letter at CALM position 4) + 2 = M + 2 = O
• Letter at new position 4 = (Letter at CALM position 3) + 2 = L + 2 = N

Thus, the resulting letter cluster is CEON.

Revision Table for Analogy Pattern

Applying to CALM:

Assembling the target word based on its positions 1, 2, 3, 4: C, E, O, N. The word is CEON.

Additional Information on Letter Analogies

Letter analogies are common in reasoning tests and involve identifying the relationship between sets of letters. The relationships can be based on various rules:

• Alphabetical Position: Adding, subtracting, or multiplying the position number of letters.
• Skip Letter Pattern: Skipping a fixed number of letters in the sequence.
• Reverse Alphabetical Order: Using the position from the end of the alphabet (Z=1, Y=2, etc.).
• Vowel/Consonant Pattern: Rules applied specifically to vowels or consonants.
• Reordering or Reversal: The letters in the second cluster are a rearrangement or reversal of the transformed letters from the first cluster.
• Combination of Rules: A pattern might involve both a transformation (like adding a number) and a rearrangement.

Solving these problems requires careful observation, listing the letters and their positions, trying out different common patterns, and checking consistency.