How to Solve Reasoning Inequalities Problems: Tips & Tricks

How to Solve Reasoning Inequalities
In this post, We will show you all that "How to solve Questions of Inequalities in just few seconds". In inequalities we do the comparison between two elements / persons / animals / things / anything in terms of age / weight / height / richness / poorness / anything. In this post, we will show you comparison in terms of age of the persons in family which will help you in understanding the thing that what is actually happening when we compare.

In inequalities, there are five symbols to represent the comparison between two persons which are >, <, =, ≥ and ≤. Out of which there symbols >, < and = are the perfect symbols which shows yes only this comparison is in between two person. Remaining two symbols are mixed up which are ≥ and ≤. ≥ shows either > or = so we can not say which one is occurring independently because > and = both have same chance to happening. Similarly ≤ shows either < or = so we can not say which one is occurring independently because < and = both have same chance to happening. Now see the Representation of all these Inequalities Symbols by figure:

1. Representation of  ">" (Greater than):
As we know, age of mother is always more than her daughter, so its the best representation of comparison symbol >. Meanwhile age of mother i.e.A > age of daughter i.e. B. No third symbol we can put here.


2. Representation of "<" (Less than):
























As we also know, age of daughter is always less than her mother, so its the best representation of comparison symbol <. Meanwhile age of  daughter i.e.A < age of mother i.e. B.  Here also No third symbol we can put.

3. Representation of "=" (Equal to):
























Here I have taken example Twin sister because both are born on the same day that mean both will have same age like if one is 14 years old then another one also will be 14 years old means both are equal in age. Hence, its the best representation of A=B.

4. Representation of "≥" (Either greater than or equal to):
























Age we know in our Indian culture, age of husband is either greater than the wife or age of husband is equal to wife. Do not take any exceptional case which are happening these days(क्यूंकि आजकल के लैला मजनू कहते है कि प्यार / इश्क़ / मोहोबत्त / Love / आशिक़ी / आशिक़ी -01 / आशिक़ी -02 में उम्र नहीं देखी जाती है बस जूनून देखी जाती है - इस डायलाग को यहाँ भूल जाएँ और अपने पुराने परंपरा में नतमस्तक हो जाएँ। ), also please do not take an example of our Bollywood star Aishwariya Rai Bachchan and Abhishek Bachchan. Hence, as we do not know the ages of husband and wife, so age of husband either will be > or = then his wife's age. Thus, its the best representation to explain you ≥ symbol.

5. Representation of "≤" (Either less than or equal to):
























Age we know in our Indian culture, age of wife is either less than the husband or age of wife is equal to husband's age. Hence, as we do not know the ages of husband and wife, so age of wife either will be < or = then her husband's age. Thus, its the best representation to explain you ≤ symbol.

Basics Questions of Inequalities with Ultimate Explanations

Q1. Statement: A>B>C , Conclusions: I. A>C  II. A< C

Explanations:
























Given statement can be represented as shown in the figure in terms of height. It can be seen clearly that height of A > height of B > height of C. Conclusion I is true because height of A is greater than height of C. Height of A can't be smaller than height of C, so conclusion II is false.

Q2. Statement: A>B=C , Conclusions: I. A>C  II. A< C

Explanations:
























As we can see in the figure B and C have equal height and A's height is greater than B's height it means A's height is also greater than C's height. Hence, conclusion I is true while conclusion II is false.

Q3. Statement: A > B ≥ C , Conclusions: I. A>C  II. A< C

Explanations:
























Here, we know age of grandfather is always greater than his son and his daughter-in-law, so here A>C is true conclusion while A<C is false.

Q4. Statement: B ≥ C , Conclusions: I. B>C  II. B=C

Explanations:
 
























≥ means either > or = , None of the > and = will happen independently. As we know age of husband will be either > or = his wife's age but we do not know exactly its > or =, so both the conclusions are false independently. We also know one of them must will come either > or =, so on combining both the conclusions we get B ≥ C. Hence, either conclusion I or conclusion II is true.

Q5. Statements: Salman<Kajol, Kajol ≥ Deepika , 
Conclusions: I. Salman>Kajol  II. Kajol=Deepika

Explanations: 
First of all combine, all the statements together,
Salman<Kajol≥ Deepika
Conclusion I is false because its clearly given in the statement that Salman<Kajol, Conclusion II also does not follow because Kajol ≥ Deepika. Always remember if ≥ is given then no preference can be given to > or =.

Q6. Statement: P ≥ Q ≥ R ≥ S ≥ T ≥ U ≥ V , Conclusions: I. P≥V  II. R≥T III. P>S 

Explanations: 
P ≥ Q ≥ R ≥ S ≥ T ≥ U ≥ V means P ≥ R , P ≥ S , P ≥ T , P ≥ U ,  P ≥ V

Conclusions: I. P≥V(True)  II. R≥T(True) III. P>S (False)

Q7. Statement: Angur≤Langur≤Bhangur,  
Conclusions: I. Angur≤Bhangur II. LangurBhangur

Explanations: 
Angur≤Langur≤Bhangur means Angur≤Bhangur
Conclusions: I. Angur≤Bhangur(True) II. Langur≥Bhangur(False because its opposite given in the statement)

Q8. Statement: Hello ≥ Fellow, Tellow<Bellow, Fellow=Mellow, Mellow≤Rellow , 
Conclusions: I. Hello>Tellow  II. Hello≤Tellow

Explanations: 
Hello ≥ Fellow=Mellow≤Rellow, Tellow<Bellow
As we see, no direct relation is given between Hello and Tellow. > and ≤ are universal because it has all the symbols which are present in inequality similarly ≥ and < are universal. So, here no conclusions follow independently but Either I or II follows.

Q9. Statement: Chikni>Dikni>Bikni, Conclusions: I. Chikni>Bikni  II. Bikni<Chikni

Explanations: 
Chikni>Dikni>Bikni means Chikni>Bikni and Chikni>Bikni means Bikni<Chikni
Conclusions: I. Chikni>Bikni (True) II. Bikni<Chikni(True)

Q10. Statement: Mobile ≥ TV , TV=CCTV, CCTV≥Remote>Senser=Denser 
Conclusions: I. Mobile=Denser II. CCTV>Senser III. TV<Remote

Explanations: 
On combining statement together,
Mobile ≥ TV =CCTV≥Remote>Senser=Denser
Conclusions: I. Mobile=Denser (False because we have Mobile>Denser)
II. CCTV>Senser(True)
III. TV<Remote(False because we have TV≥Remote)

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