numerical symbolic operations Model Questions & Answers, Practice Test for ssc cgl tier 1

Directions:

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

  • 'P @ Q' means P is neither greater than nor equal to Q.
  • '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 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.
  • Give answer (b) if only Conclusion II is true.
  • Give answer (c) if either Conclusion I or II is true.
  • Give answer (d) if neither Conclusion I nor II is true.
  • Give answer (e) if both Conclusions I and II are true.
Question :1

Statements: V $ D, D © R, R % F


Conclusions:
I. R % V
II. V @ F

Answer: (c)

  1. P @ Q ⇒ P ≯ Q and P ≠ Q
    hence P < Q
  2. P $ Q ⇒ P ≮ Q
    hence P > Q and P = Q ⇒ P ≥ Q
  3. P # Q ⇒ P ≮ Q and P ≯ Q
    hence P = Q
  4. P © Q ⇒ P ≯ Q
    hence P ≥ Q
    or P ≤ Q
  5. P % Q ⇒ P ≮ Q and P ≠ Q
    hence P > Q
@ ⇒ < $ ⇒ ≤
# ⇒ =© ⇒ ≥
% ⇒ >

Statements :

V $ D ⇒ V ≥ D
D © R ⇒ D ≤ R
R % F ⇒ R > F

Hence, V ≥ D ≤ R > F

Conclusions :

I. R % V ⇒ R > V ( False)
II. V @ F ⇒ V < F ( False)

Question :2

Statements: M © T, K % T, K @ N


Conclusions:
I. N % M
II. K % M

Answer: (e)

  1. P @ Q ⇒ P ≯ Q and P ≠ Q
    hence P < Q
  2. P $ Q ⇒ P ≮ Q
    hence P > Q and P = Q ⇒ P ≥ Q
  3. P # Q ⇒ P ≮ Q and P ≯ Q
    hence P = Q
  4. P © Q ⇒ P ≯ Q
    hence P ≥ Q
    or P ≤ Q
  5. P % Q ⇒ P ≮ Q and P ≠ Q
    hence P > Q
@ ⇒ < $ ⇒ ≤
# ⇒ =© ⇒ ≥
% ⇒ >

Statements :

M © T ⇒ M ≤ T
K % T K > T
K @ N K < N
Hence, M ≤ T < K < N

Conclusions :

I. N % M ⇒ N > M (True)
II. K % M ⇒ K > M (True)

Question :3

Statements: B @ E, E # S, S $ Z


Conclusions:
I. Z @ E
II. E # Z

Answer: (b)

  1. P @ Q ⇒ P ≯ Q and P ≠ Q
    hence P < Q
  2. P $ Q ⇒ P ≮ Q
    hence P > Q and P = Q ⇒ P ≥ Q
  3. P # Q ⇒ P ≮ Q and P ≯ Q
    hence P = Q
  4. P © Q ⇒ P ≯ Q
    hence P ≥ Q
    or P ≤ Q
  5. P % Q ⇒ P ≮ Q and P ≠ Q
    hence P > Q
@ ⇒ < $ ⇒ ≤
# ⇒ =© ⇒ ≥
% ⇒ >

Statements :

B @ E ⇒ B < E
E # S ⇒ E = S
S $ Z ⇒ S ≥ Z

Hence, B < E = S ≥ Z

Conclusions :

I. Z @ E Z < E ( False)
II. E # Z E = Z ( False)

Z is either smaller then E or equal to E

Question :4

Statements: H % M, N © M, N $ T


Conclusions:
I. H # T
II. H % T

Answer: (d)

  1. P @ Q ⇒ P ≯ Q and P ≠ Q
    hence P < Q
  2. P $ Q ⇒ P ≮ Q
    hence P > Q and P = Q ⇒ P ≥ Q
  3. P # Q ⇒ P ≮ Q and P ≯ Q
    hence P = Q
  4. P © Q ⇒ P ≯ Q
    hence P ≥ Q
    or P ≤ Q
  5. P % Q ⇒ P ≮ Q and P ≠ Q
    hence P > Q
@ ⇒ < $ ⇒ ≤
# ⇒ =© ⇒ ≥
% ⇒ >

Statements :

H % M ⇒ H > M
N © M ⇒ N ≤ M
N $ T ⇒ N ≥ T

Hence, H > M ≥ N ≥ T

Conclusions :

I. H # T ⇒ H = T (False)
II. H % T ⇒ H > T (True)

Question :5

Statements: J # R, R % K, K @ D


Conclusions:
I. K @ J
II. D @ J

Answer: (a)

  1. P @ Q ⇒ P ≯ Q and P ≠ Q
    hence P < Q
  2. P $ Q ⇒ P ≮ Q
    hence P > Q and P = Q ⇒ P ≥ Q
  3. P # Q ⇒ P ≮ Q and P ≯ Q
    hence P = Q
  4. P © Q ⇒ P ≯ Q
    hence P ≥ Q
    or P ≤ Q
  5. P % Q ⇒ P ≮ Q and P ≠ Q
    hence P > Q
@ ⇒ < $ ⇒ ≤
# ⇒ =© ⇒ ≥
% ⇒ >

Statements :

J # R J = R
R % K R > K
K @ D K < D

Hence, J = R > K < D

Conclusions :

I. K @ J ⇒ K < J (True)
II. D @ J ⇒ D < J ( False)

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