Reasoning Quiz – Coded Inequalities – 8

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Directions (Qs. 1 – 5): In the following questions, the symbols @, ©, ★, $ and # are used with the following meaning:

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

‘P © Q’ means ‘P is not smaller than Q’.

‘P★Q’ means ‘P is not greater than Q’.

‘P $ Q’ means ‘P is neither smaller than nor greater than Q’.

‘P # Q’ means ‘P is neither greater than nor equal to Q’.

Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? Give answer

(a) if only conclusion I is true.

(b) if only conclusion II is true.

(c) if either conclusion I or II is true.

(d) if neither conclusion I nor II is true.

(e) if both conclusions I and II are true.

  1. Statements:

Z # N, F © N, F ★ K

Conclusion :

(I) K $ N

(II) K @ Z

 

Answer

Option: B

Explanation:

Z < N ….(i); F ≥ N …. (ii); F ≤ K ….(iii) Combining all, we get

K ≥ F ≥ N > Z → K = N and K > Z

Hence, conclusion I (K = N) is not necessarily true but conclusion II (K > Z) is true.

 

 

  1. Statements:

D $ T, T © M, M # K

Conclusion:

(I) M $ D

(II) D @ M

Answer

Option: C

Explanation:

D = T ….(i); T ≥ M ….(ii); M < K … (iii) Combining (i) and (ii), we get

D = T ≥ M → D ≥ M → D = M or D > M

Hence, either conclusion I (M = D) or conclusion II (D > M) is true.

 

 

  1. Statements:

W © A, B ★ A, B @ M

Conclusions:

(I) B # W

(II) W $ B

Answer

Option: C

Explanation:

W ≥ A …(i); B ≤ A …. (ii); B > M … (iii) Combining all, we get

W ≥ A ≥ B > M → B ≤ W

→ B < W or B = W

Hence, either conclusion I or II is true.

 

  1. Statements:

J ★ M, M $ N, N # T

Conclusions:

(I) T @ J

(II) T $ J

Answer

Option: A

Explanation:

J ≤ M ….(i); M = N …(ii); N < T …. (iii)

Combining all, we get

J ≤ M = N < T → T > J

Hence, only conclusion I is true

 

  1. Statements:

V ★ F, F @ R, R © G

Conclusions:

(I) G # V

(II) G @ V

Answer

Option: D

Explanation:

V ≤ F …. (i); F > R …. (ii); R ≥ G ….(iii)

Combining (ii) and (iii), we get F > R ≥ G ….(iv)

Comparing (i) and (iv), we can’t get any specific relationship between G and V. Hence, both conclusions are not true.

 

 

Directions (Qs. 6-10): In the following questions, the symbols #, $, @, * and © are used with the following meaning as illustrated below:

‘P # Q’ means ‘P is not smaller than Q’

‘P $ Q’ means `P is neither smaller than nor greater than Q’

‘P @ Q’ means `P is neither greater than nor equal to Q’

‘P * Q’ means `P is not greater than Q’

‘P © Q’ means ‘P is neither smaller than nor equal to Q’

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

(a) if only Conclusion I is true.

(b) if only Conclusion II is true.

(c) if either Conclusion I or II is true.

(d) if neither Conclusion I nor II is true.

(e) if both Conclusions I and II are true.

 

 

  1. Statements:

B $ K, K @ D, D # M

Conclusions:

(I) B $ M

(II) B @ M

Answer

Option: D

Explanation:

B = K …(i);

K < D …(ii);

D ≥ M …(iii)

From (i) and (ii), we get

D > K = B …(iv)

From (iii) and (iv), no specific relation can be obtained between B and M. Therefore, B = M (Conclusion I) and B < M (Conclusion II) are not necessarily true.

 

  1. Statements:

H @ N, N © W, W # V

Conclusions:

(I) H @ V

(II) V @ N

Answer

Option: B

Explanation:

H < N … (i)

N > W …(ii);

W ≥ V …(iii)

From (ii) and (iii), we get

N > W ≥ V …(iv)

From (i) and (iv), no specific relation can be obtained between H and V. Hence, H < V (Conclusion I) is not necessarily true. But V < N (Conclusion II) follows from equation (iv).

 

  1. Statements:

J * D, Q # D, Q @ M

Conclusions:

(I) Q © J

(II) Q $ J

Answer

Option: C

Explanation:

J ≤ D …(i);

Q ≥ D …(ii);

Q < M …(iii)

Combining (i) and (ii), we get

Q ≥ D ≥ J → Q > J (Conclusion I) or Q = J (Conclusion II)

Hence, either conclusion I or conclusion II is true.

 

  1. Statements:

F # G, N $ G, N © T

Conclusions:

(I) T © F

(II) N * F

Answer

Option: B

Explanation:

F ≥ G …(i);

N = G … (ii);

N > T … (iii)

Combining all, we get

F ≥ G = N > T → N ≤ F (Conclusion II) and T < F.

Hence, conclusion I (T > F) is not true but conclusion II is true.

 

  1. Statements:

M © R, R @ K , K $ T

Conclusions:

(I) T © R

(II) T © M

Answer

Option: A

Explanation:

M > R …(i);

R < K …(ii);

K = T … (iii)

Combining (ii) and (iii), we get

K= T > R

→ T > R (Conclusion I).

On the basis of the given information no specific relation can be obtained between T and M. Hence, T > M (Conclusion II) is not necessarily true.