Understanding Letter Analogies

Letter analogies are based on relationships between letters, often using their positions in the alphabet. To solve this analogy, we first need to figure out the pattern connecting the pairs in the given sequence: MTA : JQX : GNU.

Analyzing the Pattern in MTA : JQX : GNU

Let's look at the alphabetical position of each letter in the words MTA, JQX, and GNU.

• MTA: M is the 13th letter, T is the 20th, A is the 1st. Positions: (13, 20, 1).
• JQX: J is the 10th letter, Q is the 17th, X is the 24th. Positions: (10, 17, 24).
• GNU: G is the 7th letter, N is the 14th, U is the 21st. Positions: (7, 14, 21).

Now, let's find the difference in letter positions between MTA and JQX:

• M (13) to J (10): \(10 - 13 = -3\)
• T (20) to Q (17): \(17 - 20 = -3\)
• A (1) to X (24): A is 1st. Moving back 3 letters from A is Z (26), Y (25), X (24). So the difference is -3.

The relationship between MTA and JQX is a shift of \(-3\) positions for each letter.

Next, let's find the difference in letter positions between MTA and GNU:

• M (13) to G (7): \(7 - 13 = -6\)
• T (20) to N (14): \(14 - 20 = -6\)
• A (1) to U (21): A is 1st. Moving back 6 letters from A is Z, Y, X, W, V, U. So the difference is -6.

The relationship between MTA and GNU is a shift of \(-6\) positions for each letter.

So the pattern in the given triplet (MTA : JQX : GNU) is:

• The second word (JQX) is formed by shifting each letter of the first word (MTA) backward by 3 positions.
• The third word (GNU) is formed by shifting each letter of the first word (MTA) backward by 6 positions.

Applying the Pattern to the Options

We need to find an option (ABC : DEF : GHI) that follows the same pattern: DEF is ABC shifted by \(-3\), and GHI is ABC shifted by \(-6\).

Let's check Option 2: EOY : BLV : YIS

• EOY: E=5, O=15, Y=25. Positions: (5, 15, 25).
• BLV: B=2, L=12, V=22. Positions: (2, 12, 22).
• YIS: Y=25, I=9, S=19. Positions: (25, 9, 19).

Check the relationship between EOY and BLV:

• E (5) to B (2): \(2 - 5 = -3\)
• O (15) to L (12): \(12 - 15 = -3\)
• Y (25) to V (22): \(22 - 25 = -3\)

This matches the \(-3\) shift.

Check the relationship between EOY and YIS:

• E (5) to Y (25): E is 5th. Shifting back 6 positions from E is Y (E → D → C → B → A → Z → Y). This is a \(-6\) shift.
• O (15) to I (9): \(9 - 15 = -6\)
• Y (25) to S (19): \(19 - 25 = -6\)

This matches the \(-6\) shift.

Since Option 2 (EOY : BLV : YIS) follows the same \(-3\) and \(-6\) shift pattern from the first word to the second and third words respectively, it is the correct answer.

Checking other options would show they do not follow the same pattern based on the first shift (should be -3):

• Option 1 (FNY : NML): F(6) to N(14) is \(+8\), not \(-3\).
• Option 3 (EMR : DNF): E(5) to D(4) is \(-1\), not \(-3\).
• Option 4 (ENY : CKD): E(5) to C(3) is \(-2\), not \(-3\).

Conclusion

The pair EOY : BLV : YIS is related on the same basis as the pair MTA : JQX : GNU, with letter position shifts of \(-3\) and \(-6\).

Revision Table: Letter Analogy Pattern

Additional Information on Letter Analogies

Letter analogies can use various patterns based on the English alphabet. Some common types include:

• Position Shift: Adding or subtracting a fixed number from the letter's position (like in this question). The shift can be positive or negative.
• Jumping Letters: Skipping a specific number of letters between corresponding positions.
• Reverse Alphabetical Order: Using the position from the end of the alphabet (Z=1, Y=2, etc.).
• Vowel/Consonant Patterns: Relationships based on whether letters are vowels or consonants.
• Sum or Product of Positions: Relationships based on calculations involving the letter positions.
• Mirror Image: Relationships like A is related to Z, B to Y, etc.

Solving letter analogies often requires checking the pattern letter by letter and position by position, considering the cyclic nature of the alphabet (after Z comes A). Practice with different types of letter puzzles helps in quickly identifying the underlying rule.