AAO Exam -CT 1: Reasoning (Mathematical Inequalities)

AAO Exam -CT 1: Reasoning (Mathematical Inequalities)

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AAO Exam -CT 1: Reasoning (Mathematical Inequalities)

DIRECTIONS: In the following question assuming the given statements to be true, find which of the conclusion among the given conclusions is/are definitely true and then give your answers accordingly.

Statements : T ≥ I, S < B, T = B, I > J

Conclusions :

I. B > J

II. T > S

  • Only conclusion I follows
  • Only conclusion II follows
  • Either conclusion I or II follows
  • Both conclusion I and II follow
  • Neither conclusion I nor II follows

Given Statements : T ≥ I, S < B, T = B, I > J

On combining :   S < B = T ≥ I > J

I. B > J → True (as B = T ≥  I > J, it is definitely true, Hence B > J is true )

II. T > S → True ( as T = B > S, it is definitely true, Hence T > S is true )

since both the conclusions are definitely true.

Hence, Both I and II follows.

In each of the following questions, assuming the given statements to be true, find which of the following options holds true: Give answer-

Statement: C > M, M < K, T = K, T > L

Conclusions:

I: T > M

II:  K > L

  • If conclusion I follows.

  • If conclusion II follows.

  • If either conclusion I or II follows.

  • If neither conclusion I nor II follows.

  • If both conclusions I and II follow.

According to the given information-

Statement:  > M, M < K, T = K, T > L

On combining we get: C > M < K = T > L

Conclusions:

I: T > M → True (It is given that T is greater than M, which is true according to the given question)

II: K > L → Ture (It is given that K is greater than L, which is true according to the given question)

If both conclusions I and II follow.

Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is / are definitely true and then give your answers accordingly.

Statement: P > Q < U ≤ Y < W = T > K < I 

Conclusions:

I. U < T

II. U = T

  • Only Conclusion I follows
  • Only Conclusion II follows
  • Either conclusion I or II follows
  • Neither Conclusion I nor II follows
  • Both Conclusion I and II follows

Given Statement: P > Q < U ≤ Y < W = T > K < I 

Conclusions:

I. U < T → True (U ≤ Y < W = T, U < T)

II. U = T → False (U ≤ Y < W = T, U < T)

Hence, Only I follows.

Direction: In the following question assuming the given statements to be true, find which of the conclusion among given some conclusion is/are definitely true and then give your answers accordingly:

Statement:

C < R < I ≤ S ≤ E ≤ A = N > O < G < Y > B ≥ D

Conclusions:

I. C < G

II. R < O

III. I > O

  • Only Conclusion I is true
  • Only Conclusion II is true
  • Only Conclusion III is true
  • All are true
  • None is true

Statement:

C < R < I ≤ S ≤ E ≤ A = N > O < G < Y > B ≥ D

Conclusions:

I. C < N → False (C < R < I ≤ S ≤ E ≤ A = N > O < G → No definite relation between the two can be determined)

II. R < O → False (R < I ≤ S ≤ E ≤ A = N > O → No definite relation between the two can be determined)

III. I > O → False (I ≤ S ≤ E ≤ A = N > O → No definite relation between the two can be determined)

Hence, None is true.

Direction: In the following question assuming the given statements to be true, find which of the conclusion among given some conclusion is/are definitely true and then give your answers accordingly:

Statement:

C < R < I ≤ T ≤ S = Y > P ≥ A < L < D < F ≥ G ≥ H

Conclusions:

I. Y > C

II. Y > D 

III. I < A 

  • Only Conclusion I is True
  • Only Conclusion II is True
  • Only Conclusion III is True
  • Both Conclusion I and II is True
  • Both Conclusion I and IIi is True

Statement:

C < R < I ≤ T ≤ S = Y > P ≥ A < L < D < F ≥ G ≥ H

Conclusions:

I. Y > C → True (C < R < I ≤ T ≤ S = Y → C < Y also, Y > C)

II. Y > D → False (Y > P ≥ A < L < D, as definite relationship between Y and D cannot be determined).

III. I < A → False (I ≤ T ≤ S = Y > P ≥ A , as definite relationship between I and A cannot be determined).

Hence, Only conclusion I is true

Direction: In the following question assuming the given statements to be true, find which of the conclusion among given some conclusion is/are definitely true and then give your answers accordingly:

Statement:

P = I > T > H > Z = R ≥ W > K ≥ Y > A < Q > X

Conclusions:

I. P > W 

II. H = K 

III. T > A 

  • Only Conclusion I is True
  • Only Conclusion II is True
  • Only Conclusion III is True
  • Both Conclusion I and III is true
  • All Conclusion I, II and III is True

Statement:

P = I > T > H > Z = R ≥ W > K ≥ Y > A < Q > X

Conclusions:

I. P > W → True (P = I > T > H > Z = R ≥ W → P > W)

II. H = K → False (H > Z = R ≥ W > K → H > K)

III. T > A → True (T > H > Z = R ≥ W > K ≥ Y > A → T > A)

Hence, Both Conclusion I and III are true

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statements:

B < U = S ≤ T ≤ A = N < D < I > G ≥ E > O = W

Conclusions:

I. B < D

II. A > O

  • Only Conclusion I follows
  • Only Conclusion II follows
  • Both Conclusion I and II follows
  • Either Conclusion I or Conclusion 2 follows
  • Neither Conclusion I nor II follows

Given:

Statements:

B < U = S ≤ T ≤ A = N < D < I > G ≥ E > O = W

Conclusions:

I. B < D → True (B < U = S ≤ T ≤ A = N < D → B < D)

II. A > O → False (A = N < D < I > G ≥ E > O → As the signs between A and O are opposite so, no definite relation between can be determined)

Hence, only conclusion I follows.

Directions: In the following question, assume the given statements to be true, find which of the conclusions among given conclusions is/are definitely true, and then give your answers accordingly.

Statements: A = B < C ≤ D, E > D, E > F > G ≥ H

Conclusions: 

I. A > E

II. C ≥ H

  • Only conclusion I follows
  • Only conclusion II follows
  • Either conclusion I or II follows
  • Neither conclusion I or II follows
  • Both conclusion I and II follows

Given statements: A = B < C ≤ D, E > D, F > G ≥ H

On combining: A = B < C ≤ D < E > F > G ≥ H

Conclusions: 

I. A > E → False ( A = B < C ≤ D < E)

II. C ≥ H → False (C ≤ D < E > F > G ≥ H, no relation between C and H can be determined)

Hence, Neither conclusion I or II follows

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true, and then give your answers accordingly.

Statements: 9 = 8 < 3 ≥ 5 > 2; 3 ≤ 1 = 6 ≥ 7 > 4

Conclusions:

I. 2 < 1 

II. 9 ≥ 7

  • Only conclusions I follows
  • Only conclusions II follows
  • Either conclusions I or II follows
  • Neither conclusions I or II follows
  • Both conclusions I and II follows

Given statements: 9 = 8 < 3 ≥ 5 > 2; 3 ≤ 1 = 6 ≥ 7 > 4

On combining: 9 = 8 < 3 ≤ 1 = 6 ≥ 7 > 4; 3 ≥ 5 > 2

I. 2 < 1 → True (2 < 5 ≤ 3 ≤ 1 → 2 < 1)

II. 9 ≥ 7 → False (9 = 8 < 3 ≤ 1 = 6 ≥ 7 → As relation between them cannot be determined)

Hence,  only conclusion I follow is the correct answer.

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true, and then give your answers accordingly.

Statements: P < X > R ≤ U < S = T ≤ L = M ≤ N ≥ H = I

Conclusions:

I.  S < N

II. S = N

  • Only I is true
  • Only II is true
  • Both I and II is true
  • Either I or II is true
  • Neither I nor II is true

Given Statements: P < X > R ≤ U < S = T ≤ L = M ≤ N ≥ H = I

Conclusions: 

I. S < N → False (S = T ≤ L = M ≤ N  → S ≤ N)

II. S = N → False (S = T ≤ L = M ≤ N  → S ≤ N)

For either - or condition,

S ≤ N means S < N or S = N

So, conclusion 1 and conclusion 2 forms complementary pair.

Hence, Either I or II is True is the correct answer.

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