On a cost sheet, a manager is filling in numbers on eleven lines — J, N, O, P, S, T, U, W, X, V, and Z — according to the following instructions and no others:
1. Line J must be derived from lines N, O, and V as N plus O minus V.
2. Line T must be derived from lines P and S as P plus S.
3. Line W must be derived from lines T and U as T minus U.
4. Line X must be derived from lines W and J as W minus J.
5. Line V must be derived from line T as five percent of T (i.e., 0.05 × T).
6. Line Z must be derived from line X as half of X (i.e., X/2).
Question
Details & Answer Choices
1
V cannot be derived unless which of the following is known?
(A) J
(B) N
(C) O
(D) P
(E) U
2
J cannot be derived unless which of the following is known?
(A) S
(B) U
(C) W
(D) X
(E) Z
3
It is necessary for the manager to know O before the manager can derive
(A) T
(B) U
(C) W
(D) X
(E) V
4
If the manager knows P, O, S, and U but not N, which of the following is a pair of lines that the manager can derive?
(A) J and V
(B) T and W
(C) T and X
(D) X and V
(E) X and Z
✅ Correct Answers (Analytical Reasoning Q#83):
1. (D) P → V depends on T (V = 0.05×T) and T depends on P and S; thus P is essential.
2. (A) S → J requires N, O, V; but V requires T which requires S (T = P+S). So without S, T unknown → V unknown → J unknown.
3. (E) V → O is directly used in J formula, but to derive V, O is not needed? Wait: V = 5% of T; T needs P & S; O appears only in J. But J is not required for V. Actually re-evaluation: V does NOT require O, but the question asks “necessary to know O before manager can derive _____”. Which derived line requires O? J requires O (N+O-V). So to derive J, O must be known. However, choices: T, U, W, X, V. X = W-J, J needs O. Hence X needs O indirectly. But only V is independent of O? Among the listed, V does NOT need O. However the question: "It is necessary to know O before the manager can derive _____" means: For which line among options, O is a prerequisite? X depends on J which depends on O. So X cannot be derived without O. Similarly J not in options. The official logic: X requires W and J; J requires O. Thus O is necessary for X. So answer (D) X. Also V can be derived without O. So correct = X.
4. (E) X and Z → Given P, O, S, U (no N). T = P+S (known), V = 0.05×T (known), W = T-U (known). J = N+O-V (cannot derive because N missing). X = W - J → J missing so X cannot be derived? Wait, but if N is missing, J unknown → X unknown. But the pair that can be derived: T (yes), W (yes), V (yes), Z? Z = X/2, but X requires W and J, J unknown so Z unknown. However X requires J, so not derivable. Let's re-check: Without N, J not derivable. So X not derivable. But option (E) says X and Z, which is not possible. Option (B) T and W: both derivable (T from P,S ; W from T,U). That pair is possible. Also (A) J and V: J needs N missing, so no. (C) T and X: X not derivable. (D) X and V: X not derivable. (E) X and Z: both need X not derivable. So correct should be T and W = option (B). After full dependency: given P,O,S,U but NO N. J requires N so J not derivable. X requires J so X not derivable. Z requires X so not derivable. V requires T which is derivable (P+S) → V derivable. T derivable, W derivable. So the only pair fully derivable is (B) T and W. Therefore correct answer for Q4 = B.
📘 Summary: Q1: P, Q2: S, Q3: X, Q4: T and W (Option B).
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