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**Instructions**

In the following question, the relationship between different elements is given along with two conclusions. Find out the conclusion which definitely follows from the given relationship and choose the option accordingly.

**Question 1:Â **$ X>Y=Z ; S>Q>R ; Z>P=Q $

Conclusion I : $ X>Q$

Conclusion II: $ S=Z $

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 2:Â **$A \geq H \geq L \geq Q; F > G; Q = U = Y > F;$

Conclusion I : $H \geq Y $

Conclusion II: $Q < A$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 3:Â **$E = F \geq T \geq R; Q > J = O; Q < Z < R$

Conclusion I : $Z < F$

Conclusion II: $T >O$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

IBPS PO Quant Formulas & Shortcuts

**Question 4:Â **$F \geq K > Z \geq P; W > V \geq D; P = W$

Conclusion I : $Z \geq D$

Conclusion II: $F\leq V$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 5:Â **$X < Y \leq Z< W; M > N \geq W; X > K$

Conclusion I : $N > X$

Conclusion II: $Y < M$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Instructions**

In the following question, the relationship between different elements is given along with two conclusions. Find out the conclusion which definitely follows from the given relationship and choose the option accordingly.

**Question 6:Â **$X < Y = Z \leq G; C > B = D; D > G$

Conclusion I : $Z < B$

Conclusion II: $C > Y$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 7:Â **$A > H \geq L \geq Q; F > G; Q > U = Y > F;$

Conclusion I : $H \geq F$

Conclusion II: $Q < A$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 8:Â **$H = W \geq G \geq K; J > B = O; J < P < K$

Conclusion I : $P < W$

Conclusion II: $G \geq O$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 9:Â **$A > H > Y \geq T; O > L = X; T = O$

Conclusion I : $Y \geq X$

Conclusion II: $A \leq L$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 10:Â **$A < B = C \leq D; O > E = D; A > P$

Conclusion I : $E > A$

Conclusion II: $B < O$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Instructions**

In the following question, the relationship between different elements is given along with two conclusions. Find out the conclusion which definitely follows from the given relationship and choose the option accordingly.

**Question 11:Â **$X > Y \leq Z$ ; $Y= P \geq Q$ ; $Q= R> S$

Conclusion I : $X>S$

Conclusion II: $Z\geq R$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 12:Â **$X=Y\geq Z ; Z=A< B ; Q < P \leq Z$

Conclusion I : $ X>P$

Conclusion II: $B> Q$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 13:Â **$L\leq M\geq N; L=X\geq Y; P<N>Q$

Conclusion I : $M>P$

Conclusion II: $M\geq Y$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 14:Â **$P<Q>R , P>X>Y , R>L>M$

Conclusion I: $Y<Q$

Conclusion II: $P=R$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

**Question 15:Â **$I=J\leq K; J\geq A=B; B>C>D$

Conclusion I : $K \geq B$

Conclusion II: $J \geq B$

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Both the conclusions follow

d)Â Either conclusion I or conclusion II follows

e)Â None of the conclusions follows

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**Answers & Solutions:**

**1)Â AnswerÂ (A)**

$X>Y=Z>P=Q$. Thus, $X>Q$. Hence, Conclusion 1 follows.

No relation can be established between S and Z. Thus, Conclusion 2 does not follow.

Hence, option A is the correct answer.

**2)Â AnswerÂ (A)**

$H \geq L \geq Q=U=Y $. Thus, $H \geq Y $. Hence, conclusion 1 follows

$A\geq H \geq L \geq Q$. Thus, $A\geq Q$. Hence, conclusion 2 does not follow.

Hence, option A is the correct answer.

**3)Â AnswerÂ (C)**

$ F\geq T\geq R>Z $. Thus, $ Z>F $. Hence, conclusion 1 follows.

$ T\geq R>Z>Q>J=O$. Thus, $T>O$. Hence, conclusion 2 follows.

Thus, both the conclusion follows.

Hence, option C is the correct answer.

**4)Â AnswerÂ (E)**

$Z\geq P=W>V\geq D$. Thus, $Z>D$. Hence, conclusion 1 does not follow

$F\geq K > Z\geq P=W>V$. Thus, $F>V$. Hence, conclusion 2 does not follow.

Thus, none of the conclusion follows.

Hence, option E is the correct answer.

**5)Â AnswerÂ (C)**

$N\geq W>Z\geq Y>X$. Thus, $N>X$. Hence, conclusion 1 follows.

$M>N\geq W>Z\geq Y$. Thus, $M>Y$. Hence, conclusion 2 follows.

Thus, both the conclusions follows.

Hence, option C is the correct answer.

**6)Â AnswerÂ (C)**

From $X < Y = Z \leq G$; and $D > G$; we can say that $D > G \geq Z = Y > X$.

From $D > G \geq Z = Y > X$ and $C > B = D$ we can say that $C > B = D > G \geq Z = Y > X$.

We can see that both the conclusions are true. Therefore, option C is the correct answer.

**7)Â AnswerÂ (B)**

From $A > H \geq L \geq Q$; and $Q > U = Y > F$; we can say that $A > H \geq L \geq Q > U = Y > F$.

From $A > H \geq L \geq Q > U = Y > F$ and $F > G$ we can say that $A > H \geq L \geq Q > U = Y > F > G$.

In conclusion I, it should be $H > F$, hence conclusion I is incorrect.

We can see that only conclusion II is true. Therefore, option b is the correct answer.

**8)Â AnswerÂ (A)**

From $H = W \geq G \geq K$; and $J < P < K$; we can say that $H = W \geq G \geq K > P > J$.

From $H = W \geq G \geq K > P > J$ and $J > B = O$ we can say that $H = W \geq G \geq K > P > J > B = O$.

In conclusion II, it should be $G > O$, hence conclusion II is incorrect.

We can see that only conclusion I is true. Therefore, option A is the correct answer.

**9)Â AnswerÂ (E)**

From $A > H > Y \geq T$; and $T = O$; we can say that $A > H > Y \geq T = O$.

From $A > H > Y \geq T = O$ and $O > L = X$ we can say that $A > H > Y \geq T = O > L = X$.

In conclusion I, it should be $Y > X$, hence conclusion I is incorrect.

In conclusion II, it should be $A > L$, hence conclusion II is incorrect.

We can see that no conclusion I is true. Therefore, option E is the correct answer.

**10)Â AnswerÂ (C)**

From $A < B = C \leq D$; and $A > P$; we can say that $D \geq C = B > A > P$.

From $D \geq C = B > A > P$ and $O > E = D$ we can say that $O > E = D \geq C = B > A > P$.

We can see that both the conclusions are true. Therefore, option C is the correct answer.

**11)Â AnswerÂ (C)**

$X>Y=P\geq Q=R> S$. Hence, $X>S$. Therefore, conclusion 1 follows.

$Z\geq Y = P \geq Q=R$ i.e. $Z\geq R$.Therefore, conclusion 2 follows.

Hence, option C is the correct answer.

**12)Â AnswerÂ (B)**

$X=Y\geq Z\geq P $ i.e. $X\geq P$. Hence, conclusion I does not follow.

$B>A=Z\geq P>Q $ i.e. $B>Q$. Hence, conclusion II follows

Hence, option B is the correct answer.

**13)Â AnswerÂ (C)**

$M\geq N>P $ i.e. $M>P$. Therefore, conclusion 1 follows.

$ M\geq L = X\geq Y$ i.e. $M\geq Y$. Therefore, conclusion 2 follows

Hence, option C is the correct answer.

**14)Â AnswerÂ (A)**

$Q>P>X>Y$ i.e. $Q>Y$.Therefore, conclusion 1 follows.

No relation between P and R can be established. Thus, conclusion 2 does not follow.

Hence, option A is the correct answer.

**15)Â AnswerÂ (C)**

$K\geq J\geq A=B$ i.e. $K\geq B$.

$K\geq J\geq A=B$ i.e. $J \geq B$. Therefore both the conclusions follow.

Hence, option C is the correct answer.