Directions: Each question or group of questions is based on a passage, graph, table, or set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. For each question, select the best answer choice given.
Questions 11-15
A government is assigning each of six embassy office workers - Farr, Golden, Hayakawa, Inserra, Jones, and Kovacs - to embassies. There are four embassies. Embassies L and M are located in countries with dry climates, whereas embassies P and T are located in countries with humid climates. The office workers must be assigned according to the following rules:
Each embassy must have at least one of the workers assigned to it.
At least one embassy in a humid climate must have at least two workers assigned to it.
Golden cannot be assigned to the same embassy as Kovacs.
Inserra must be assigned to an embassy in a dry climate.
Jones must be assigned to an embassy in a humid climate.
11. Which of the following is an acceptable assignment of the workers to the embassies?
L | M | P | T | |
|---|---|---|---|---|
A. | Farr, Golden | Inserra, Kovacs | Hayakawa | Jones |
B. | Golden, Kovacs | Inserra | Jones | Farr, Hayakawa |
C. | Golden | Farr, Inserra | Kovacs | Jones, Hayakawa |
D. | Jones | Golden, Inserra | Hayakawa | Farr, Kovacs |
E. | Kovacs | Farr, Hayakawa | Inserra | Golden, Jones |
12. Which of the following must be assigned either to embassy L or to embassy M?
13. Which of the following CANNOT be true?
14. If Golden and Kovacs are assigned to L and M, respectively, which of the following must be true?
15. If Golden, Hayakawa, and Kovacs are among the workers assigned to embassies in humid climates, which of the following must be true?
- (A) Farr is assigned to an embassy to which none of the other five office workers is assigned.
- (B) Golden is assigned to an embassy to which none of the other five office workers is assigned.
- (C) Jones is assigned to the same embassy as Kovacs.
- (D) Hayakawa is assigned to the same embassy as Golden.
- (E) Hayakawa is assigned to the same embassy as Kovacs.
Detailed Explanation (in Bangla)
Answer Keys
Question | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|
Answer | C | D | D | A | A |
Explanations
Let’s keep the notation short: F(arr), G(olden), H(ayakawa), I(nserra), J(ones), K(ovacs).
Dry embassies = L, M Humid embassies = P, T
Global rules (copy these into your scratch work)
Every embassy gets ≥ 1 worker.
At least one humid embassy gets ≥ 2 workers.
G and K cannot be together.
I = dry (L or M).
J = humid (P or T).
11. Which row is acceptable? (Answer C)
Check each choice against the five rules.
Choice | L (dry) | M (dry) | P (humid) | T (humid) | Quick check |
|---|---|---|---|---|---|
A | F, G | I, K | H | J | I is in humid? ✗ (Rule 4) |
B | G, K | I | J | F, H | G with K ✗ (Rule 3) |
C | G | F, I | K | J, H | All five rules satisfied ✓ |
D | J | G, I | H | F, K | J in dry ✗ (Rule 5) |
E | K | F, H | I | G, J | I in humid ✗ (Rule 4) |
Only row C survives every test.
12. Who must go to L or M? (Answer D - Inserra)
I is explicitly required to be in a dry embassy (rule 4).
Everyone else may appear in either climate (J must be humid, but that doesn’t force L/M).
Therefore Inserra is the one worker that is guaranteed to be placed in L or M.
13. Which scenario cannot occur? (Answer D - “Three workers are assigned to M”)
Try the impossible case:
If three workers occupy M, there are only three people left for L, P, T.
L still needs ≥ 1 worker → at most two people remain for the two humid embassies.
For rule 2 to hold, those two would both have to go to the same humid embassy (to make “≥ 2”).
That would leave the other humid embassy empty, breaking rule 1.
So “3 in M” is impossible; the other four counts (A, B, C, E) can be arranged without contradiction.
14. G in L and K in M — what must follow? (Answer A - “Farr is in P or T”)
Set up the board:
Dry: L = G, … M = K, …
Left to place: F, H, I, J
Requirements: I = dry, J = humid; every embassy filled; ≥ 2 people in one humid.
Reason it out:
Put I in one of the dry embassies (L or M).
That fills both dry embassies, so only humid spots remain.
To satisfy rule 2 we must get at least two workers into the humid group. We already have to place J there, so at least one of the two remaining people (F or H) must also be humid.
If we try to keep F in dry, the humid group would be {J, H}. They would both have to sit together (to make “≥ 2”), leaving the other humid embassy empty — impossible.
Therefore F has to move into P or T.
Thus, “Farr is assigned to P or T” is forced; none of the other answer choices is always necessary.
15. G, H, K are all humid - what must be true? (Answer A - “Farr is alone at his embassy”)
Facts:
Humid group now contains G, H, K, plus J (rule 5) → total four people in P & T.
G cannot share with K, so they must split between P and T.
That leaves two humid slots to fill the “≥ 2” requirement - the simplest way is to pair one of {H, J} with G and the other with K. (There are several legal pairings.)
Dry embassies:
Only I and F can be placed in dry embassies (L and M) because all four others are now humid.
L and M each need ≥ 1 worker.
So I must occupy one dry embassy and F must occupy the other - alone, because no one else is allowed to join them there.
Hence Farr is necessarily assigned to an embassy “to which none of the other five office workers is assigned.”
Options B-E are all avoidable with simple counter-examples, but (A) holds in every permissible arrangement.