# Inequalities – Beginner Series – Set 2

D.1-5) In each of the following questions, relationship between different elements is shown in the statements followed by two conclusions. Study the statements carefully and answer the below questions.

Q.1) Statements:

M≤Q<R=S; S>T≥V

Conclusions:

I.V<R     II.M>T

a) If conclusion I follows.

b) If conclusion II follows.

c) If either Conclusions I or II follows.

d) If neither Conclusions I nor II follows.

e) If both Conclusions I and II follow.

(a)

M ≤ Q < R = S > T ≥ V

I.V < R         (True)

II.M > T       (False)

Q.2) Statements:

A≤C<D≤E=F; R≥G>E

Conclusions:

I.F>R           II.A<G

a) If conclusion I follows.

b) If conclusion II follows.

c) If either Conclusions I or II follows.

d) If neither Conclusions I nor II follows.

e) If both Conclusions I and II follow.

(b)

I.F > R         (False)

II.A < G       (True)

Q.3) Statements:

P=Q<R≤T; Q≤Y=A≥C

Conclusions:

I.P<A           II.A≥P

a) If conclusion I follows.

b) If conclusion II follows.

c) If either Conclusions I or II follows.

d) If neither Conclusions I nor II follows.

e) If both Conclusions I and II follow.

(b)

I.P < A         (False)

II.A ≥ P        (True)

Q.4) Statements:

M = R≤ J≤ K; J < I ≤ P > G

Conclusions:

I.M<G          II.G ≤ M

a) If conclusion I follows.

b) If conclusion II follows.

c) If either Conclusions I or II follows.

d) If neither Conclusions I nor II follows.

e) If both Conclusions I and II follow.

(c)

Q.5) Statements:

K ≤L=O, P≥Q > L, R > P = N

Conclusions:

I.P > K         II.N > L

a) If conclusion I follows.

b) If conclusion II follows.

c) If either Conclusions I or II follows.

d) If neither Conclusions I nor II follows.

e) If both Conclusions I and II follow.

(e)

I.P > K         (True)

II.N > L        (True)

D.6-10) In the following questions, the symbols %, \$, @, *, # are used with the following meanings as illustrated below.

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

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

‘A * B’ means ‘A is neither greater than nor smaller than B’.

‘A # B’ means ‘A is not greater than B’.

‘A \$ B’ means ‘A is not smaller than B’.

Q.6) If the conclusions ‘B % N’ and ‘V \$ L’ is definitely true, then which of the following statement logically satisfies the conclusion?

a) L \$ Q @ N * O @ V % B * T

b) B % T % O @ N % V \$ Q * L

c) T \$ B % O * N # V \$ Q * L

d) L * B * T % O @ V @ N * Q

e) None of these.

(c)

T ≥ B < O = N ≤ V ≥ Q = L

I.B < N        (True)

II.V ≥ L        (True)

Q.7) If the following conclusion W % O and U @ T should always true, then which of the following statements logically satisfies the given conclusions?

a) W # J \$ U # O # P * T % I

b) I * J * O % R # U @ W % T

c) O @ J * P % I @ W % U * T

d) W # J * P % O \$ U * I @ T

e) None of these.

(d)

W ≤ J = P < O ≥ U = I > T

I.W < O       (True)

II.U > T       (True)

Q.8) If the following conclusions B % U and I # H should always true, then which of the following statements logically satisfies the given conclusions?

a) I % B % S * C % L \$ J *H % U

b) B \$ L # S * J # I % U @ C * H

c) L @ B % S * U \$ I # J * H @ C

d) H * B % C @ S % I \$ J * L @ U

e) None of these.

(c)

L > B < S = U ≥ I ≤ J = H > C

I.B < U        (True)

II.I ≤ H        (True)

Q.9) In the following conclusions L # B should be false and B \$ I should be true. Then which of the following statements logically satisfies the given conclusions?

a) B @ P % I * J #H \$ M @ L # F

b) I \$ P % L * J \$ F \$ M % I * B

c) M* P # B @ H # J # F @ L * I

d) H @ P % L * J # B \$ M * I # F

e) None of these.

(e)

None of these

Q.10) In the following conclusions, C @ N should be false and N \$ H should be true. Then which of the following statements logically satisfies the given conclusions?

a) N % B % M * C \$ V @ H * S # O

b) C @ M * B @ H \$ V * O @ S * N

c) C @ M @ B % N \$ V \$ H * S # O

d) C * M @ B % H \$ V % S @ N @ O

e) None of these