Mathematical and Computer Operations - Verbal Reasoning Questions and Answers with solutions or explanation for interview, entrance tests and competitive exams. Practice online quiz, fully solved examples with detailed answers.

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

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'P$Q' means 'P is not greater than Q'.

'P@Q' means 'P is neither smaller than nor equal to Q'.

'P%Q' means 'P is neither greater than not equal to Q'.

'P©Q' means 'P is not smaller than Q'.

'P#Q' means 'P is neither greater than nor smaller than Q'.

Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

Statements: M @ R, R © K, J % K

Conclusions: I. M @ J II. J % R III. K % M

Answer: Option E

Explanation:

M > R --- (i) R ≥ K --- (ii) J < K --- (iii)

combining (i), (ii) and (iii), we get:

M > R ≥ K > J => M > J (conclusion I),

R > J (conclusion II),

M > K (conclusion III),

Hence, conclusion I (M > J), conclusion II (J < R) and conclusion III (K < M) are all true.

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

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'P$Q' means 'P is not greater than Q'.

'P@Q' means 'P is neither smaller than nor equal to Q'.

'P%Q' means 'P is neither greater than not equal to Q'.

'P©Q' means 'P is not smaller than Q'.

'P#Q' means 'P is neither greater than nor smaller than Q'.

Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

Statements: D © N, N # V, W $ V

Conclusions: I. D # W II. W % D III. V #

Answer: Option B

Explanation:

D ≥ N -- (i) N = V -- (ii) W ≤ V -- (iii)

combining (i) and (ii), we get:

D ≥ N = V => D ≥ N. Hence, conclusion III (V = D) is not necessary true.

Again, combining all (i), (ii) and (iii), we get

D ≥ N = V ≥ W => D ≥ W. Hence, neither conclusion I (D = W) or conclusion II (W < D) is true. But both conclusion I (D = W) and conclusion II (W

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

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'P$Q' means 'P is not greater than Q'.

'P@Q' means 'P is neither smaller than nor equal to Q'.

'P%Q' means 'P is neither greater than not equal to Q'.

'P©Q' means 'P is not smaller than Q'.

'P#Q' means 'P is neither greater than nor smaller than Q'.

Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

Statements: H % B, M © B, K # M

Conclusions: I. K @ H II. B # K III. K @ B

Answer: Option D

Explanation:

H < B -- (i) M ≥ B -- (ii) K + M -- (iii)

combining (ii) and (iii), we get:

K = M ≥ B => K ≥ B. Hence, neither conclusion II (B = K) or conclusion III (K > B) is true. But, both conclusion I and II together make a complementary pair. Hence, either conclusion II (B = K) or conclusion III (K > B) is true.

Again combining all (i), (ii) and (iii) we get K = M ≥ B > H => K > H (conclusion I). Hence conclusion I (K > H) is true.

4. In the following questions, the symbols @, #, $, % and © are used with the following meaning as illustrated below:Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

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'P$Q' means 'P is not greater than Q'.

'P@Q' means 'P is neither smaller than nor equal to Q'.

'P%Q' means 'P is neither greater than not equal to Q'.

'P©Q' means 'P is not smaller than Q'.

'P#Q' means 'P is neither greater than nor smaller than Q'.

Statements: V © M, N % V, J @ N

Conclusions: I. J @ M II. M @ N III. V @ J

Answer: Option A

Explanation:

V ≥ M -- (i) N < V -- (ii) J > N -- (iii)

From (i) and (ii), no specific relation between M and N can be established. Hence, conclusion II (M > N) is not necessarily true.

Again, from (i), (ii) and (iii), no specific relation between V and J can be established. Hence, conclusion III (V > J) is not necessarily true.

5. In the following questions, the symbols @, #, $, % and © are used with the following meaning as illustrated below:Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.

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'P$Q' means 'P is not greater than Q'.

'P@Q' means 'P is neither smaller than nor equal to Q'.

'P%Q' means 'P is neither greater than not equal to Q'.

'P©Q' means 'P is not smaller than Q'.

'P#Q' means 'P is neither greater than nor smaller than Q'.

Statements: T # R, R $ W, W % H

Conclusions: I. H @ R II. H @ T III. H © T

Answer: Option C

Explanation:

T = R -- (i) R < W -- (ii) W < H -- (iii)

combining (ii) and (iii), we get

H > W ≥ R => H > T (conclusion II). Hence, conclusion II (H ≥ T) is true but conclusion III (H ≥ T) is not true.