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Coded Inequalities

Question

In the following questions, the symbols @, #, %, $ and * are used with the following meaning as illustrated below.

‘A @ B’ means ‘A is not smaller than B’

‘A # B’ means ‘A is neither smaller than nor equal to B’

‘A % B’ means ‘A is neither smaller than nor greater than B’

‘A $ B’ means ‘A is not greater than B’

‘A * B’ means ‘A is neither greater than nor equal to B’

Statements: F% G, H * I, D # F, G @ H

Conclusion:I. D # H II. G @ D III. I $ G

A Only conclusion I and II are true Correct Answer Incorrect Answer
B Only conclusion II and III are true Correct Answer Incorrect Answer
C Only conclusion III is true Correct Answer Incorrect Answer
D Only conclusion I is true Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

Solution

Decoded statement: F = G, H < I, D > F, G ≥ H Decoded conclusion: I. D > H       II.G ≥ D                 III. I ≤ G Combined Inequalities: I > H ≤ F = G < D I > H ≤ F = G < D                                H < D. Hence conclusion I is true. I > H ≤ F = G < D                               G < D. Hence conclusion II is not true. I > H ≤ F = G < D                              No relationship can be established between I and G. Hence conclusion III is not true.

Question

Statements: P % Q, Q $ B, B * C, N $ C

Conclusion:I. P % B II. B # P III. Q @ N

A Either conclusion I or II is true Correct Answer Incorrect Answer
B Only conclusion II and III are true Correct Answer Incorrect Answer
C Only conclusion III is true Correct Answer Incorrect Answer
D Only conclusion I is true Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

Solution

Decoded statement: P = Q, Q ≤ B, B < C, C ≥ N Decoded conclusion: I. P = B      II.B > P                III. Q ≥ N Combined Inequalities: P = Q ≤ B < C ≥ N P = Q ≤ B < C ≥ N             Q ≤ B. Hence either conclusion I or II is true. P = Q ≤ B < C ≥ N            No relationship can be established between Q and N. Hence conclusion III is not true

Question

Statements: G @ H, E # F, F % G, D # E

Conclusion:I. F # H II. F % H III.D # H

A Only conclusion II is true Correct Answer Incorrect Answer
B Only conclusion II and III are true Correct Answer Incorrect Answer
C Only conclusion I is true Correct Answer Incorrect Answer
D Either conclusion I or II and III are true Correct Answer Incorrect Answer
E None is true Correct Answer Incorrect Answer

Solution

Decoded statement: G ≥ H, E > F, F = G, D > E Decoded conclusion: I. F > H       II.F = H                 III. D > H Combined Inequalities: D > E > F = G ≥ H D > E > F = G ≥ H                                F ≥ H. Hence either conclusion I or II is true. D > E > F = G ≥ H                             D > H. Hence conclusion III is true.

Question

Statements: A @ B, Y $ Z, X * Y, Z * A

Conclusion:I. X $ A II. A % Y III. Z # Y

A Only conclusion II is true Correct Answer Incorrect Answer
B Only conclusion II and III are true Correct Answer Incorrect Answer
C Only conclusion I is true Correct Answer Incorrect Answer
D Either conclusion I or II and III are true Correct Answer Incorrect Answer
E None is true Correct Answer Incorrect Answer

Solution

Decoded statement: A ≥ B, Y ≤ A, X < Y, Z < A Decoded conclusion: I. X ≤ A      II.A = Y                 III. Z > Y Combined Inequalities: X < Y ≤ A ≥ B   OR  Z < A ≥ Y > X X < Y ≤ A ≥ B                      X < A. Hence conclusion I is not true. X < Y ≤ A ≥ B                       Y ≤ A. Hence conclusion II is not true.  Z < A ≥ Y > X                      No relationship can be established between Z and Y. Hence conclusion III is not true.

Question

Statements:  P % Q, Q $ R, R @ S, O * P

Conclusion:  I. P @ S       II. R # O         III. S # P

A Only conclusion II is true Correct Answer Incorrect Answer
B Only conclusion II and III are true Correct Answer Incorrect Answer
C Only conclusion I is true Correct Answer Incorrect Answer
D Either conclusion I or III and II are true Correct Answer Incorrect Answer
E None is true Correct Answer Incorrect Answer

Solution

Decoded statement: P = Q, Q ≤ R, R ≥ S, O < P Decoded conclusion: I. P ≥ S                        II.R > O                III. S > P Combined Inequalities: O < P = Q ≤ R ≥ S O < P = Q ≤ R ≥ S              No relationship can be established between P and S. Hence either conclusion I or III is true. O < P = Q ≤ R ≥ S             R > O. Hence conclusion II is true.

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