Shortcut Tricks To Solve Inequalities

Inequality is a common topic for all competitive exams especially SNAP and CMAT and CET. There always 5 to 6 questions come in all competitive exams out of this topic. In Inequality, we are given some directions, a statements followed by 4 conclusions. We have to find the conclusions which are true according to the given statement. In Exams mostly questions comes in two forms: 1) Coded Inequality. 2) Direct Inequality. In Direct Inequality, they use direct symbols <, >, =, ≤, and ≥ in the statement. In Coded Inequality form, $, #, %, &, @ symbols are used. PART I: Direct Inequality: Meanings of Different Direct Inequality symbols used in the Problems: 1)     < : Less than 2)     ≤ : Less than or Equal to 3)     > : Greater than 4)     ≥ : Greater than or Equal to 5)     = : Equal to When solving Direct inequalities, we will consider the following cases:- Case 1: Equal to The first step in every equation is to ignore equal. Yes ignore. Please read the following example to know why we want you to ignore ‘equal to’ sign: Example 1: A =B <C =D Therefore, A < D Example 2: A < B =C Therefore, A < C. Case 2: Same Sign When same sign repeats itself again and again, then such sign would be the answer. Example 3: A < B < C < D Therefore, A < D Example 4: A= B ≥ C = D ≥ E Therefore, A ≥ E Case 3: Common Sign (= is never considered as a common sign). So, the every first thing is to ignore (=) as ignore told in Case 1. Example 5: A < B ≤ C Therefore, A < C. Example 6: A ≥ B > C = D ≥ E > F Therefore, A > F. Case 4: Opposite Sign Whenever there are opposite sign there are 3 possibilities. For instance, A > B ≤ C (No relation), there will be 3 possibilities: A = C A > C A < C SIGN POSSIBILITIES ≤ <, = ≥ ≥, = = <, >, = Example 7: A < B ≤ C = D ≤ E Conclusion 1: A < E Conclusion 2: A ≤ E Conclusion 3: A > D Conclusion 4: B = E In this question, only Conclusion 1 follows. Conclusion 2 is wrong because common sign between A and E is <. Conclusion 3 is wrong because A < D. Conclusion 4 is wrong because B ≤ E. ( B = E is just a possibility) PART II: Coded Inequality: Let us take we have given the following directions: A $ B means A is not smaller than B 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 Now first you have to decode the meanings of different symbols given- Solve it one by one: 1) First we have Given, A is not smaller than B that means A can either be equal to A or Greater than B i.e A ≥ B. 2) A is neither smaller than nor equal to B that means A is Greater than B i.e A > B. 3) A is neither greater than nor equal to B that means A is lesser than B i.e A < B. 4) A is neither greater than nor smaller than B that means A equal to B i.e A = B. 5) A is not greater than B that means A can either be equal to or lesser than B i.e A ≤ B. Let us take the following example: 1).Statements: K & B, B $ W, W # H, H % M Conclusions: (1) M @ W.  (2)  H @ K.  (3) W & K. Step 1: First Make a single statement. K & B $ W # H % M Step 2: Now we have to analyze the given conclusions one by one. 1)     M @ W Ø  If you go from M to W, you will go in a Reverse Direction i.e to the Left hand Side. Ø  Between M and W there are present two symbols, one is % and other is #. Ø  In the above table both the symbols are present in row 2 & the Highest Priority symbol is #. Ø  Since the direction of letters formed was to the Left Hand Side, So In Left Hand Side case we should note the symbol which is exactly above the symbol #. Ø  The symbol above to # is @. Ø  And in conclusion the symbol present between M and W is also @. So M @ W is TRUE. 2)     H @ K Ø  If you go from H to K, you will go in a Reverse Direction i.e to the Left hand Side. Ø  Between H and K, the symbols present are #, $, and &. Ø  Check these symbols with the above table, # is in Row 2 and $ is in Row 1.Both the symbols are in different rows. Ø  So Conclusion 2 is FALSE. 3)    W & K Ø  From W to K, the direction is to the Left hand side, Ø  Between W and K, the symbols present are $ and & and the higher priority symbol is $. Ø  Direction is to the Left-hand side. So we should note the symbol which is opposite to $. That is %. Ø  But given conclusion is W & K. So it is FALSE Therefore Conclusion 1 alone Follows Let us take one more example: 2) Statement: H @ T, T # F, F & E, E % V. Conclusions: 1) V $ F.   2) E @ T.   3) H @ V.   4) T # V Modified Single Statement: H @ T # F & E % V 1) V $ F: Left Hand Side Direction – Symbols present are % and &. Both are in Row 2. Since the direction is Left Hand Side, and highest priority symbol is %, we should note the symbol which is exactly opposite to % which is symbol is $. So the Conclusion 1 is True. 2) E @ T:Left Hand Side Direction. Symbols  present are & and #. Both are in Row 2. High priority symbol is #. Symbol opposite to # is @. So E @ T is True. 3) H @ V:Right Hand Side Direction. Symbols  present are @, #, & and % but are in different rows. So False. 4) T # V:Right Hand Side Direction. Symbols are #, &, and %. All are present in Row 2. High Priority symbol is #. So T # V is True. (In Right Hand Direction case we should check for the same symbol not the opposite one) Therefore, In this Conclusion 1, 2, and 4 are True.