Inequality Questions and Answers

Answer: A

Correct answer: if only conclusion I is true

Translating: M < T, T > K, K = D. Conclusion I asks whether D < T, and D = K < T gives it directly. Conclusion II asks how K compares with M, but both lie below T with no link between them, so nothing follows.

Answer: B

Correct answer: only conclusion II is true

Translating: R ≤ N, N ≥ F, F > B. Conclusion II asks whether B < N, and B < F ≤ N gives it. Conclusion I asks whether F = R, but R and F both lie below N with no relation to one another, so it cannot be established.

Answer: D

Correct answer: neither conclusion I or II is true

Translating: H > W, W < M, M ≥ K. The chain reverses at W, which is the smallest element named, so H and M are each above it with no link between them, and K sits below M with no link to W. Neither conclusion can be reached.

Answer: E

Correct answer: both conclusion I and II is true

Translating: R ≥ T, T = M, M > D, giving one unbroken chain R ≥ T = M > D. Conclusion I follows since D < M = T, and conclusion II since R ≥ T = M. An unbroken chain with no reversal is what allows both to be established.

Answer: D

Correct answer: neither conclusion I or II is true

Translating: F ≥ K, K < B, B ≤ M. The chain reverses at K, so F sits above it on one side and B and M above it on the other, with nothing joining the two branches. Neither M nor B can therefore be compared with F.

Answer: B

Correct answer: S < R

From R > O, O = A and A > S the chain runs R > O = A > S without reversal, so R > S. Everything involving T fails, since S < T points away from the rest of the chain and leaves T unconnected to R, O and A.

Answer: D

Correct answer: >

The expression is \( P > L \;?\; A \ge N = T \), and both \( P > A \) and \( T < L \) must be definitely true. Test the keyed symbol first. With \(\ge\) the line reads \( P > L \ge A \ge N = T \). That does give \( P > A \), but for the second requirement it gives only \( T = N \le A \le L \), that is \( T \le L \); taking \( L = A = N = T \) satisfies every statement while making \( T < L \) false, so \(\ge\) fails. With \(>\) the line reads \( P > L > A \ge N = T \). Now \( P > L > A \) gives \( P > A \), and \( T \le A < L \) gives \( T < L \) - both hold, and the answer is \(>\). The remaining choices reverse the chain at L: \(<\) or \(\le\) leaves P and A unrelated, since both would then sit above L rather than in a single chain.

Answer: D

Correct answer: >, =, =, >=

Substituting the keyed symbols into \( B \_ L \_ O \_ N \_ D \) gives \[ B > L = O = N \ge D. \] For \( B > N \): L, O and N are all equal, and B exceeds L, so \( B > N \) - definitely true. For \( D \le L \): the last link gives \( N \ge D \), and \( N = L \), so \( D \le L \) - definitely true. The other sets break one requirement or the other. The first, \( =,=,\ge,\ge \), makes \( B = L \), so \( B > N \) cannot be guaranteed. The third, \( >,<,=,\le \), points L below O and so leaves B and N unlinked. One caveat worth noticing: the set \( >,=,\ge,> \) yields \( B > L = O \ge N > D \), which also makes both required expressions true, so this item admits more than one working answer.

Answer: E

Correct answer: P, N, A, L

Filling the blanks gives P < N < A > L, from which A > N > P and therefore A > P. The expression asked for is one making A < P definitely false, and establishing the opposite relation is what does that - leaving the two unrelated would make it undetermined rather than false.

Answer: C

Correct answer: < , =, = , <

The symbols give F < O = U = N < D. From F < O = N comes F < N, so F > N is definitely false; and from U = N < D comes U < D, so U > D is definitely false. Both statements are required to be false, which needs the opposite relation established in each case rather than merely left open.