Mathematical operation and symbol notation
Direction: In the following questions, the symbols @, $, #, © and % are used with the following meanings as illustrated below.
'P $ Q' means 'P is not smaller than Q'.
'P © Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means 'P is neither smaller than nor equal to Q'.
'P % Q' means 'P' is not greater 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 four Conclusions I, II, III and IV given below them is/are definitely true and given your answer accordingly.
- Statements ::
T % R, R $ M, M @ D, D © H
Conclusions ::
I. D % R
II. H # R
III. T © M
IV. T % D
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Statements
T % R ⇒ T ≤ R
R $ M ⇒ R ≥ M
M @ D ⇒ M = D
D © H ⇒ D < H
i.e., T ≤ R ≥ M = D < H
Conclusions
I. D % R ⇒ D ≤ R (✔)
II. H # R ⇒ H > R (x)
III. T ©M ⇒ T < M (x)
IV. T % D ⇒ T ≤ D (x)Correct Option: A
Statements
T % R ⇒ T ≤ R
R $ M ⇒ R ≥ M
M @ D ⇒ M = D
D © H ⇒ D < H
i.e., T ≤ R ≥ M = D < H
Conclusions
I. D % R ⇒ D ≤ R (✔)
II. H # R ⇒ H > R (x)
III. T ©M ⇒ T < M (x)
IV. T % D ⇒ T ≤ D (x)
Hence conclusion I is definitely true.
- Statements ::
R # J, J $ D, D @ K, K % T
Conclusions ::
I. T # D
II. T @ D
III. R # K
IV. J $ T
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Statements
R # J ⇒ R >J
J $ D ⇒ J ≥ D
D @ K ⇒ D = K
K % T ⇒ K ≤ T
i.e., R > J ≥ D = K ≤ T
Conclusions
I. T # D ⇒ T > D (may be)
II. T @ D ⇒ T = D (may be)
III. R # K ⇒ R > K (✔)
IV. J $ T ⇒ J ≥ T (x)
Hence, either conclusion I or II and III are definitely true.Correct Option: D
Statements
R # J ⇒ R >J
J $ D ⇒ J ≥ D
D @ K ⇒ D = K
K % T ⇒ K ≤ T
i.e., R > J ≥ D = K ≤ T
Conclusions
I. T # D ⇒ T > D (may be)
II. T @ D ⇒ T = D (may be)
III. R # K ⇒ R > K (✔)
IV. J $ T ⇒ J ≥ T (x)
Hence, either conclusion I or II and III are definitely true.
Direction: In these questions, relationships between different elements is shown in the statement. The statement is followed by two conclusions. Study the conclusions based on the given statement and select the appropriate answer.
- Statement ::
Z ≥ Y = W ≥ X
Conclusions ::
I. W < Z
II. W = Z
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Z ≥ Y = W ≥ X
Conclusions
I. W < Z (✔)
or
II. W = Z (✔)
Thus, either Conclusion I or II follows.Correct Option: D
Z ≥ Y = W ≥ X
Conclusions
I. W < Z (✔)
or
II. W = Z (✔)
Thus, either Conclusion I or II follows.
- Statements
L > M,
M > N,
N > P.
Conclusions
I. L > P
II. M > P
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Given that,
L > M ....(I)
M > N .....(II)
N > P .....(II)
On combining all the three statements, we get
L > M > N > P
Conclusions
I. L > P (true)
II. M > P (true)Correct Option: E
Given that,
L > M ....(I)
M > N .....(II)
N > P .....(II)
On combining all the three statements, we get
L > M > N > P
Conclusions
I. L > P (true)
II. M > P (true)
So, it is clear that both Conclusions I and II follow from the given statements.
Direction: In these questions, relationship between different elements is shown in the statements. These statements are followed by two conclusions.
- Statements
B < C, D > B, C > K, K ≤ N, N < B
Conclusions
I. C > N
II. B > K
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Conclusion
I. C > N (✔)
II. B > N (✔)Correct Option: D
Conclusion
I. C > N (✔)
II. B > N (✔)
