Test: Inequalities - 1 - ACT MCQ

Given statements: A > B, B > C, C = D, D < E

On combining: A > B > C = D < E

Conclusions:

I. B = D → False (as B > C = D → B > D thus clear relation between B and D)

II. B > D→ True (as B > C = D → B > D)

Therefore, only conclusion II is True.

Given statements: L > F = S < T ≤ Q < P

I. F < Q → True (as F = S < T ≤ Q)

II. L > S → True (as L > F = S)

III. T < P → True (as T ≤ Q < P)

Hence, all of the given conclusions follow.

Given statement: P > S ≥ M = L < J = N

I. L < N → True (as L < J = N)

II. P > M → True (as P > S ≥ M)

III. S = L → False (as S ≥ M = L gives either S = L or S > L)

Hence, both conclusions I and II are true.

Statement: S = U > K > L ≥ Y < R ≤ B

Conclusion:

I. K < Y → False (As, S = U > K > L ≥ Y)

II. L > Y → False (As, S = U > K > L ≥ Y)

III. L = Y → False (As, S = U > K > L ≥ Y)

But conclusion II and III forms a complementary pair.

Hence, either conclusion II or III follows.

Given: W > X, X > Y and Y > Z

On combining: W > X > Y > Z

I) X > Z → True

II) W > Z → True

III) Z > W → False (as W > Z)

IV) W > Y → True

Hence, Z > W is definitely wrong.

Statements: P ≥ R, R > T, T ≤ A

Conclusions:

I. P > A → False (As P ≥ R > T ≤ A → Thus, there is no clear relationship given between P and A)

II. T < P → True (As P ≥ R > T → T < P)

Hence, Only conclusion II follows.

Given statements: P < Q < R; R = S ≤ T

On combining: P < Q < R = S ≤ T

Conclusions:

I. Q > T → False (as Q < R and R = S ≤ T → Q < R = S ≤ T → Q ≤ T)

II. S > P → True (as P < Q < R; R = S → P < Q < R = S → P < S)

Hence, only conclusion II is true.

I. M > Q → False (as Q ≤ C ≤ B = M → M gives either M = Q or M > Q).

II. D ≤ Q → False (as Q ≤ C ≤ B = M > D)

III. M = Q → False (as Q ≤ C ≤ B = M → M gives either M = Q or M > Q).

IV. C < D → False (as C ≤ B = M > D).

P > Q ≤ C ≤ B = M > D is given in statement. Therefore but Conclusion I and III forms a complementary pair for either.

Thus, the correct answer is option 1.

Given statements: P > Q; Q > R; R > S; S > T.

On combining: P > Q > R > S > T

Conclusions

I. T < Q → True (as Q > R > S > T → Q > T)

II. R < P → True (as P > Q > R → P > R)

Hence, both of the conclusions are true.

Given statements: B > C; C E; E > F

On combining: B > C < D > E < F

Conclusions:

I. C < F → False (as C < D > E < F → clear relationship between F and D cannot be determined)

II. B > D → False (as B > C < D → clear relation between B and D cannot be determined)

Hence, none of the conclusions is true.