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Inequalities is one of the most important topics in the CMAT, and also it is an important section. One can utilize this article which consists of the most important questions regarding Inequalities. Cracku provides you with the Top 20 very Important Inequalities Questions for CMAT based on the questions asked in previous exam papers. Click on the link below to download the Inequalities Questions for CMAT PDF with detailed answers.

Instructions

For each of the following five questions, the prices of various items are shown by inequalities. The statement in each question is followed by 2 conclusions. Based on the information in the statement, which of the conclusions are implied?

Question 1:Â Statement $Ketch up > Iodised salt \geq Tomatoes \geq Eggs$ and Oranges < Radish < Ketch up
Conclusions 1) Radish < eggs 2) Oranges < Tomatoes

a)Â Neither of the conclusion is implied.

b)Â Conclusion 2 is implied but conclusion 1 is not

c)Â Conclusion 1 is implied but conclusion 2 is not

d)Â Both the conclusions are implied.

e)Â Either conclusion 1 or conclusion 2 is implied but both are not.

Solution:

Statement $Ketch up > Iodised salt \geq Tomatoes \geq Eggs$ and Oranges < Radish < Ketch up

=> $oranges < radish < ketchup> iodized salt \geq tomatoes \geq eggs$

As there is no direct relation between oranges and tomatoes and between radishes and eggs, we cannot conclude either of the conclusions.
So, both the conclusions are false.

Question 2:Â Cat < Lion < Ostrich = Otter = Dove $\geq$ Salmon > Yak
Conclusions 1) Ostrich > Yak 2) Cat < Dove

a)Â Neither of the conclusion is implied.

b)Â Conclusion 2 is implied but conclusion 1 is not

c)Â Conclusion 1 is implied but conclusion 2 is not

d)Â Both the conclusions are implied.

e)Â Either conclusion 1 or conclusion 2 is implied but both are not.

Solution:

Cat < Lion < Ostrich = Otter = Dove $\geq$ Salmon > Yak

Hence, Ostrich > Yak and Cat < Dove.
So, both the conclusions are implied.

Question 3:Â $Ketchup \geq Lemons > Mango \geq Neem$
Conclusions 1) $Neem \leq Ketch up$2) Neem < Ketchup

a)Â Neither of the conclusion is implied.

b)Â Conclusion 2 is implied but conclusion 1 is not

c)Â Conclusion 1 is implied but conclusion 2 is not

d)Â Both the conclusions are implied.

e)Â Either conclusion 1 or conclusion 2 is implied but both are not.

Solution:

$Ketchup \geq Lemons > Mango \geq Neem$

Hence, Ketchup > Neem
So, conclusion 2 is implied.

Question 4:Â $zebra \geq yak = whale \leq xray$
conclusions 1) whale < zebra 2) whale = zebra

a)Â Neither of the conclusion is implied.

b)Â Conclusion 2 is implied but conclusion 1 is not

c)Â Conclusion 1 is implied but conclusion 2 is not

d)Â Both the conclusions are implied.

e)Â Either conclusion 1 or conclusion 2 is implied but both are not.

Solution:

$zebra \geq yak = whale \leq xray$

Hence, $whale \leq zebra$ => whale = zebra or whale < zebra

So, either of the two conclusions are implied.

Question 5:Â Banana> apple> salmon, carrot > lemon > yak milk
conclusions 1) banana > lemon 2) apple > yak milk

a)Â Neither of the conclusion is implied.

b)Â Conclusion 2 is implied but conclusion 1 is not

c)Â Conclusion 1 is implied but conclusion 2 is not

d)Â Both the conclusions are implied.

e)Â Either conclusion 1 or conclusion 2 is implied but both are not.

Solution:

Banana> apple> salmon and carrot > lemon > yak milk
As there is not direct link between the two, neither of the conclusions is implied.

Instructions

In these questions, relationships between different elements is shown in the statements. The statements is followed by two conclusions. Study the conclusions based on the given statement and select the appropriate answer.

Question 6:Â Statement: K > I $\geq$ T $\geq$ E; O < R < K
Conclusions: I. R < E 2. O < T

a)Â Neither conclusion I nor II follows

b)Â Both conclusions I and II follows

c)Â Only conclusion II follows

d)Â Either conclusion I or II follows

e)Â Only conclusion I follows

Solution:

According to the given inequalities, K is largest among all but nothing specific can be said about O,R,I,T and E. Hence, no conclusion can be drawn from the given information. So answer will be A

Question 7:Â Statement C < L < O = U = D $\geq$ S > Y
Conclusions I. O > Y II. C<D

a)Â Neither conclusion I nor II follows

b)Â Both conclusions I and II follows

c)Â Only conclusion I follows

d)Â Either conclusion II follows

e)Â Only conclusion I or II follows

Solution:

As it is given in statement 1 that O=U=D which is greater than S, Y, L and C hence, the conclusions O>Y and C<D can drawn from the given statements.

Question 8:Â Statement K $\geq$ L > M $\geq$ N
Conclusions I. N $\leq$ K II. N<K

a)Â Both conclusions I and II follows

b)Â Neither conclusion I nor II follows

c)Â Either conclusion II or II follows

d)Â Only conclusion I follows

e)Â Only conclusion II follows

Solution:

In conclusion 1, it is given that N<=K. That’s not possible as N is less than or equal to M which is absolutely less than K. Conclusion 2 is valid as it mentions that N < K. Hence, only conclusion 2 will follow.

Question 9:Â Statement: Z $\geq$ Y = W $\geq$ X
Conclusions I. W<Z II. W=Z

a)Â Only conclusion II follows

b)Â Only conclusion I follows

c)Â Neither conclusion I nor II follows

d)Â Either conclusion I or II follows

e)Â Both conclusions I and II follows

Solution:

According to the given statement Z>= Y and Y=W So Z>=W

Hence, anyone of the conclusion might be followed. Hence, answer will be D

Question 10:Â Statement: B > A > S < I > C > L >Y
Conclusions I. B>L II. A>Y

a)Â Only conclusion I follows

b)Â Only conclusion II follows

c)Â Either conclusion II or II follows

d)Â Neither conclusion I nor II follows

e)Â Both conclusions I and II follows

Solution:

According to the given inequalities, nothing certain can be said about B, L and A, Y as no absolute measurement can be drawn from the given inequalities. Hence, answer will be D

Instructions

In these questions, the relationship between different elements is shown in the statements. The statements are followed by two conclusions. Give answer

Question 11:Â Statements: $F < R\geq O=M\leq T=K$
Conclusions: I. $K\geq O$
II.F < M

a)Â if only conclusion I is true

b)Â if only conclusion II is true

c)Â if either conclusion I or II is true

d)Â if neither conclusion I nor II is true

e)Â if both conclusion I and II are true

Solution:

T is greater than or equal to M. But T is equal to K. K is greater than or equal to M. O is equal to M.
Therefore, K is greater than or equal to O.
Hence, conclusion I follows.
We cannot establish a relation between F and M even both are known to be less than F.
Hence, this conclusion II does not follow.

Option A is correct.

Question 12:Â Statements: $G=N\leq O\geq P>Q=R$
Conclusions: I. O >R
II. $P\leq G$

a)Â if only conclusion I is true

b)Â if only conclusion II is true

c)Â if either conclusion I or II is true

d)Â if neither conclusion I nor II is true

e)Â if both conclusion I and II are true

Solution:

I. O >R. This is a correct coclusion because Q is greater than R. P is greater than Q while I is greater than or equal to R. Hence, O is greater than R.
II. $P\leq G$. We cannot draw any conclusion between relationship of P with G.
Only conclusion I follows.
Question 13:Â Statements: $F<O=L\geq W=S$
Conclusions: I. $W\leq F$
II. $O\geq S$

a)Â if only conclusion I is true

b)Â if only conclusion II is true

c)Â if either conclusion I or II is true

d)Â if neither conclusion I nor II is true

e)Â if both conclusion I and II are true

Solution:

No relation can be established between W and F as data provided is inadequate.
L is greater than W. O is equal to L. Therfore, O is greater than W. W is equal to S.
Hence, we can say that, O is greater than S.
Option B is correct option.
Question 14:Â Statements: $B=R\geq T<O=P\geq S$
Conclusions: I. B < O
II. T < S

a)Â if only conclusion I is true

b)Â if only conclusion II is true

c)Â if either conclusion I or II is true

d)Â if neither conclusion I nor II is true

e)Â if both conclusion I and II are true

Solution:

Conclusions:
I. B < O, we cannot establish any direct relationship between B and O as no such data is provided.
II. T < S, no relationship can be established between T and S as data provided is inadequate.

Hence, conclusions I and II do not follow.
Therefore, option D is correct.

Question 15:Â Statements: $P>Q\geq A<R=I$
Conclusions:
I. A < P
II. I > A

a)Â if only conclusion I is true

b)Â if only conclusion II is true

c)Â if either conclusion I or II is true

d)Â if neither conclusion I nor II is true

e)Â if both conclusion I and II are true

Solution:

P is greater than Q which is greater than or equal to R. Hence, we can say that P is greater than R.
Hence, conclusion I follows.

R is greater than A but I and A are equal. Therefore, R is greater than I.
Hence, conclusion II follows.

Both I and II follow.
Option E is correct.

Instructions

<p “=””>In each of the following questions, relationship between different elements is shown in the statements. The statements are followed by two conclusions numbered I and II. Study the conclusions based on the given statements and select the appropriate answer.

Give answer (a) if only Conclusion I is true
Give answer (b) if neither Conclusion I nor Conclusion II is true
Give answer (c) if only Conclusion II is true
Give answer (d) if both Conclusion I and Conclusion II are true
Give answer (e) if either Conclusion I or Conclusion II is true

Question 16:Â Statements
M > A â‰¥ B = Q â‰¤ P < J â‰¤ Y = Z â‰¥ A > X
Conclusions:
I. B < Y
II. X â‰¥ J

a)Â if only Conclusion I is true

b)Â if neither Conclusion I nor Conclusion II is true

c)Â if only Conclusion II is true

d)Â if both Conclusion I and Conclusion II are true

e)Â if either Conclusion I or Conclusion II is true

Solution:

StatementÂ : M > A â‰¥ B = Q â‰¤ P < J â‰¤ Y = Z â‰¥ A > X

Conclusions:

I. B < Y : true
II. X â‰¥ J : false

Thus,Â only Conclusion I is true.

=> Ans – (A)

Question 17:Â Statements
M > A â‰¥ B = Q â‰¤ P < J â‰¤ Y = Z â‰¥ A > X
Conclusions
I. Z = Q
II. Z > Q

a)Â if only Conclusion I is true

b)Â if neither Conclusion I nor Conclusion II is true

c)Â if only Conclusion II is true

d)Â if both Conclusion I and Conclusion II are true

e)Â if either Conclusion I or Conclusion II is true

Solution:

StatementÂ :Â M > A â‰¥ B = Q â‰¤ P < J â‰¤ Y = Z â‰¥ A > X

ConclusionsÂ :

I. Z = Q : It cannot be true as J > P
II. Z > QÂ : It is true

Thus, only conclusion II is true.

Hence, option C is the correct answer.

Question 18:Â Statements
G < R = A â‰¤ S ; T < R
Conclusions
I. G < S
II. S > T

a)Â if only Conclusion I is true

b)Â if neither Conclusion I nor Conclusion II is true

c)Â if only Conclusion II is true

d)Â if both Conclusion I and Conclusion II are true

e)Â if either Conclusion I or Conclusion II is true

Solution:

StatementsÂ :Â G < R = A â‰¤ S ; T < R

=> $S\geq R>G$ and $R>T$

Conclusions :

I. G < S = true
II. S > T = true

Thus,Â both Conclusion I and Conclusion II are true.

=> Ans – (D)

Question 19:Â Statements
P = U < M < K â‰¤ I > N ; D â‰¥ P ; I â‰¥ C
Conclusions
I. M < C
II. N > U

a)Â if only Conclusion I is true

b)Â if neither Conclusion I nor Conclusion II is true

c)Â if only Conclusion II is true

d)Â if both Conclusion I and Conclusion II are true

e)Â if either Conclusion I or Conclusion II is true

Solution:

Statements :Â P = U < M < K â‰¤ I > N ; D â‰¥ P ; I â‰¥ C

ConclusionsÂ :

I. M < C = false
II. N > UÂ = false

Thus,Â neither Conclusion I nor Conclusion II is true.

=> Ans – (B)

Question 20:Â Statements
P = U < M < K â‰¤ I > N ; D â‰¥ P ; I â‰¥ C
Conclusions
I. D â‰¥ K
II. I > P

a)Â if only Conclusion I is true

b)Â if neither Conclusion I nor Conclusion II is true

c)Â if only Conclusion II is true

d)Â if both Conclusion I and Conclusion II are true

e)Â if either Conclusion I or Conclusion II is true