Directions: Read the information and answer the given questions. Six persons,…
2025
Directions: Read the information and answer the given questions.
Six persons, namely, A, B, C, D, E, and F, like different colors: Red, Blue, Green, Yellow, Black, and White, and they are showcasing their work in a painting exhibition on two different dates, either 9 or 16, of three different months: March, June, and August of the same year, but not necessarily in the same order.
The one who likes Yellow showcases immediately before D. E likes neither Red nor Green. A showcases in the month that has an even number of days. A showcases two persons after the one who likes Red. F showcases on an odd-numbered date, but after A. C showcases three persons before the one who showcases immediately after the one who likes Black. C does not showcase on an even-numbered date. A does not like Black. The one who likes Green showcases in the same month as E. Neither C nor B likes Yellow and White.
Four of the following are alike in a certain way. Who among the following does not belong to the group?
- A.
D
- B.
The one who likes Red
- C.
A
- D.
E
- E.
The one who likes Green
Show answer & explanation
Correct answer: D
Concept
In an attribute-based multi-variable arrangement puzzle, first fix the underlying linear sequence of slots implied by the fixed categories (here: three months in calendar order, each split into two dates, giving six chronological slots). Then translate every clue into a constraint on POSITION (relative order) or on an ATTRIBUTE (color) tied to a position, and resolve the slots by elimination before assigning attributes.
Application
List the six slots in chronological order: (1) March-9, (2) March-16, (3) June-9, (4) June-16, (5) August-9, (6) August-16. Only June has an even number of days (30, versus 31 for March and August), so "A showcases in the month with an even number of days" places A at slot 3 or slot 4.
"A showcases two persons after the one who likes Red" fixes the Red-liker two slots before A: if A is at slot 3, Red is at slot 1; if A is at slot 4, Red is at slot 2.
"F showcases on an odd-numbered date but after A" means F's slot has date 9 (slot 1, 3 or 5) and comes after A's slot. Testing both positions for A (slot 3 or slot 4), the only odd-dated slot after A that remains open is slot 5 (August-9) in both cases, so F is fixed at slot 5.
"C does not showcase on an even-numbered date" restricts C to slot 1, 3 or 5; slot 5 is already F's, so C is at slot 1 or slot 3.
"C showcases three persons before the one who showcases immediately after the one who likes Black" gives C's slot = (Black-liker's slot + 1) - 3, i.e. Black-liker's slot = C's slot + 2. Testing A at slot 3: C would have to be slot 1, making the Black-liker's slot = 3, which is A's own slot — but "A does not like Black", so this branch fails and A cannot be at slot 3. Hence A is at slot 4 (June-16), and Red is at slot 2 (March-16).
With A fixed at slot 4, testing C at slot 3 makes the Black-liker's slot = 5 (F). The three remaining people — B, D, E — would then occupy slots 1, 2 and 6. "The one who likes Yellow showcases immediately before D" requires a slot directly before D's slot: D at slot 1 has no slot before it, so that fails immediately. D at slot 2 would need the Yellow-liker at slot 1; the only people left for slot 1 and slot 6 are B and E, and clue 10 ("neither C nor B likes Yellow") rules out B at slot 1, so slot 1 would be E (Yellow) and slot 6 would be B. But slot 2 already carries the Red attribute (from Red at slot 2), so D would like Red at slot 2 — yet "the one who likes Green showcases in the same month as E" (March, slots 1-2) then has no slot left to carry Green, since slot 1 is Yellow and slot 2 is Red. This branch fails. D at slot 6 would need the Yellow-liker at slot 5 — but slot 5 is F, already fixed as the Black-liker in this branch, so F cannot also like Yellow. This branch fails too. All three placements for D fail, so C cannot be at slot 3; C must be at slot 1 (March-9), making the Black-liker's slot = 3.
The three people left to place — B, D and E — occupy slots 2, 3 and 6. "The one who likes Yellow showcases immediately before D" needs a slot directly before D's slot to be free for a Yellow-liker: testing D at slot 2 or slot 3 forces the Yellow-liker onto a slot that clue 10 (neither C nor B likes Yellow) or the fixed Red slot rules out, so D must be at slot 6, with the Yellow-liker at slot 5 — which is F. So F likes Yellow, and D takes the last slot, slot 6 (August-16).
B and E now share slots 2 and 3. Slot 2 already carries the Red attribute (step 5); since "E likes neither Red nor Green," E cannot sit at slot 2, so E is at slot 3 (June-9) and B is at slot 2 (March-16), making B the Red-liker.
Slot 3 is the Black-liker's slot (step 6), so E likes Black. "The one who likes Green showcases in the same month as E" (June = slots 3-4); slot 3 already has Black, so the Green-liker must be at slot 4, which is A. So A likes Green.
Only Blue and White remain, for C (slot 1) and D (slot 6). "Neither C nor B likes... White" rules out White for C, so C likes Blue and D likes White.
Final arrangement
Slot (Month-Date) | Person | Colour |
|---|---|---|
March-9 | C | Blue |
March-16 | B | Red |
June-9 | E | Black |
June-16 | A | Green |
August-9 | F | Yellow |
August-16 | D | White |
Cross-check against every clue
Yellow-liker (F, August-9) is immediately before D (August-16) — holds.
E likes Black, not Red or Green — holds.
A is in June, the even-day month — holds.
Red-liker (B, slot 2) is two slots before A (slot 4) — holds.
F's date is 9 (odd) and F's slot (5) is after A's slot (4) — holds.
C (slot 1) is three slots before the slot immediately after the Black-liker (Black at slot 3, so slot 4; 4-3=1) — holds.
C's date is 9, not even — holds.
A likes Green, not Black — holds.
Green-liker (A, June) is in the same month as E (June) — holds.
Neither C (Blue) nor B (Red) likes Yellow or White — holds.
Answer to the classification question
The grouping attribute across the five options is the SHOWCASE DATE. D showcases on the 16th, the one who likes Red (B) showcases on the 16th, A showcases on the 16th, and the one who likes Green (also A) showcases on the 16th — four instances tied to the 16th of a month. The one who does not fit this pattern is the option tied to the 9th of the month, since that person's slot carries the minority date attribute rather than the majority one shared by the rest of the set.