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. DOY:PAK ::BQM:NCY :: ILU:?
- (a)UYG
- (b)TYG
- (c)UXG
- (d)TXG
Answer
Why
Correct — C. Number the letters A=1 to Z=26 and read each analogy across, letter by letter.
DOY → PAK: D(4) → P(16), O(15) → A(1), Y(25) → K(11). Every step is +12, wrapping past Z, since 15 + 12 = 27 and 27 − 26 = 1.
BQM → NCY: B(2) → N(14), Q(17) → C(3), M(13) → Y(25). +12 again.
Rule: every letter moves 12 places forward, wrapping from Z back to A.
I(9) + 12 = 21 = U
L(12) + 12 = 24 = X
U(21) + 12 = 33, and 33 − 26 = 7 = G
That spells UXG, option (c).
Why the others are wrong
- (a)UYG — U and G are right and the middle letter is not. Y(25) is 13 places past L(12), where every letter in both sample pairs moves exactly 12.
- (b)TYG — T(20) is 11 past I and Y is 13 past L, so the two letters move by different amounts. A single shift has to apply to all three.
- (d)TXG — X and G are right, but T(20) is 11 places past I(9). An 11-step shift fails the samples too: D + 11 gives O, not P.
Concept
A constant-shift analogy moves every letter of a cluster the same number of places. Your whole job is to find that number and to handle the wrap.
Write positions above the letters, subtract, and check that the difference is the same in all three columns of both sample pairs. If one column disagrees, the rule is not a constant shift and you need a per-position pattern instead.
When a sum passes 26, subtract 26. U(21) + 12 = 33 becomes 7, which is G.
A shift of 13 is the one that undoes itself — apply it twice and you are back where you started. A shift of 12 does not, so the direction of the arrow matters here.
Key facts
- A=1 to Z=26, and any total above 26 wraps by subtracting 26.
- Every letter in DOY:PAK and BQM:NCY moves forward exactly 12 places.
- I, L and U shifted 12 forward give U, X and G.
Study next
Common traps
- Testing one letter of one pair and assuming the shift for the rest.
- Forgetting to subtract 26 after the wrap, which leaves U + 12 as position 33.
- Applying the shift backwards, which turns a +12 rule into −12.
The same analogy frame is set again at Reasoning Q.13, where each of the four positions takes its own step instead of one constant shift covering every letter (10 Sep 2024, 12:30).
Related PYQs
No directly related past PYQ was found.