# Inequalities – Beginner Series – Set 1

D.1-10) In each question, statements are given, which are followed by two conclusions I & II.You have to find out which conclusion(s) is/are definitely true.

Q.1) Statement:

T>Y, Y<W, W≥E, E≥I, I<S

Conclusions:

I.W>S          II.W≤S

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.

(c)

T > Y < W ≥ E ≥ I < S

I.W > S        (False)

II.W ≤ S      (False)

Q.2) Statement:

Y≥S, S=F, F<G, G<Q, Q=P

Conclusions:

I.Y≥F           II.F<P

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.

(e)

Y ≥ S = F < G < Q = P

I.Y ≥ F         (True)

II.F < P        (True)

Q.3) Statement:

J=K, KF, FD, D>A, A>W

Conclusions:

I.K>W          II.K=W

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.

(d)

J = K ≤ F ≤ D > A > W

I.K > W        (False)

II.K = W      (False)

Q.4) Statement: MN, W<N, I>W, M=P

Conclusions:

I.M<I           II.N≤P

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.

(b)

P = M ≥ N > W < I

I.M < I         (False)

II.N ≤ P       (True)

Q.5) Statement: LP, R<L, P=J, J>D

Conclusions:

I.L≥J            II.R>D

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.

(a)

R < L ≥ P = J > D

I.L ≥ J          (True)

II.R > D       (False)

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

‘P % Q’ means ‘P is greater than Q’

‘P \$ Q’ means ‘P is greater than or equal to Q’

‘P @ Q’ means ‘P is smaller than Q’

‘P & Q’ means ‘P is less than or equal to Q’

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

Q.6) Statements:

Q @ W, W \$ R, R # T, T % Y, Y & P Conclusions:

I.Q \$ T        II.R % Y       III.R & P

a) Only I follows

b) Only II follows

c) Only both I and III follow

d) Only both II and III follow

e) None of these

(b)

Q < W ≥ R = T > Y ≤ P

I.Q ≥ T        (False)

II.R > Y        (True)

III.R ≤ P      (False)

Q.7) Statements:

N @ M, M & V, V & C, C & H, H % A

Conclusions:

I.N & V         II.V & A        III.N & H

a) Only I follows

b) Only both II and III follow

c) Only both I and II follow

d) None follows

e) None of these

(d)

N < M ≤ V ≤ C ≤ H > A

I.N ≤ C        (False)

II.V ≤ A       (False)

III.N ≤ H      (False)

Q.8) Statements:

R \$ D, D \$ V, V # B, B @ N, N % J

Conclusions:

I.R % V        II.R # V       III.N & D

a) Only I follows

b) Only either I or II follows

c) Only III and either I or II follow

d) Only III follows

e) None of these

(b)

R ≥ D ≥ V = B < N > J

I.R > V         (False)

II.R = V       (False)

III.N ≤ D      (False)

Q.9) Statements:

I \$ K, K % M, M # J, J @ H

Conclusions:

I.M @ H       II.I % M       III.K % J

a) Only II and III follow

b) Only I follows

c) Only II follows

d) None follows

e) All I, II and III follow

(e)

I ≥ K > M = J < H

I.M < H        (True)

II.I > M        (True)

III.K > J       (True)

Q.10) Statements:

Q & W, W # U, U % M, M \$ G # N

Conclusions:

I.Q # U        II.U % N      III.U % Q

a) Only both I and II follow

b) Only I follows

c) Only II and either I or III follow

d) Only either I or III follows

e) Only II follows