Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. CWE:ZFX ::PYT:MDI :: KIL:?
- (a)PRO
- (b)RTQ
- (c)PQO
- (d)STQ
Answer
Why
Correct — B. Number the alphabet A=1 to Z=26 and add each letter to the letter it turns into.
C(3)+Z(26) = 29, W(23)+F(6) = 29, E(5)+X(24) = 29.
P(16)+M(13) = 29, Y(25)+D(4) = 29, T(20)+I(9) = 29.
Rule: every letter is replaced by the letter at position 29 minus its own.
K(11) becomes 29 − 11 = 18 = R
I(9) becomes 29 − 9 = 20 = T
L(12) becomes 29 − 12 = 17 = Q
That reads RTQ, which is option (b).
Why the others are wrong
- (a)PRO — PRO applies the plain opposite-letter rule, where a pair sums to 27: K+P = 27, I+R = 27, L+O = 27. The two sample pairs fix the total at 29, so every letter here lands two places short.
- (c)PQO — PQO rests on no single total at all: K+P = 27, but I+Q = 26 and L+O = 27. One arithmetic rule has to hold for all three letters, and no rule produces this cluster.
- (d)STQ — STQ gets the last two letters right, I+T = 29 and L+Q = 29, but not the first: K+S = 11+19 = 30, one more than the 29 the two sample pairs fix.
Concept
Letter-cluster analogies are solved by turning letters into their alphabet positions, A=1 through Z=26, and hunting for one arithmetic relation that holds for every letter of the pair.
Two families cover most of them. A fixed shift moves every letter the same number of places; a fixed sum makes each letter and its partner add to a constant.
This item is the second kind, and the constant is 29.
Read both given pairs before you commit. One pair alone can fit several rules; two rarely do.
29 is the ordinary reverse-alphabet total of 27 plus 2, so the code is also describable as 'take the opposite letter, then move two places forward'. Both descriptions reach the same three letters.
Key facts
- A=1, B=2 and so on to Z=26 — every letter-coding question starts by writing these numbers down.
- Opposite letters (A and Z, B and Y, C and X) always add to 27.
- In this set the constant is 29, so a letter maps to the one at position 29 minus its own.
Study next
Common traps
- Testing only the first pair, when CWE:ZFX alone fits several rules and PYT:MDI is what pins the total to 29.
- Reaching for the reverse alphabet, whose total of 27 produces PRO instead of RTQ.
- Accepting a rule that fits two of the three letters — it has to fit all three.
Alphabet positions also decide the series at Reasoning Q.2 and the odd-one-out at Q.13 (9 Sep 2024, 16:00).
Write the position numbers under the letters before you look at the options.
Related PYQs
No directly related past PYQ was found.