By Editorial Board Pratiyogita Darpan UPKAR PRAKASHAN, AGRA-2

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2 By Editorial Board Pratiyogita Darpan UPKAR PRAKASHAN, AGRA-2

3 Publishers Publishers UPKAR PRAKASHAN (An ISO 9001 : 2000 Company) 2/A, Swadeshi Bima Nagar, AGRA Phone : , , Fax : (0562) , care@upkar.in, Website : Branch Offices : 4845, Ansari Road, Daryaganj, New Delhi Phone : /66 28, Chowdhury Lane, Shyam Bazar, Near Metro Station, Gate No. 4 Kolkata (W.B.) Phone : Pirmohani Chowk, Kadamkuan, Patna Phone : B-33, Blunt Square, Kanpur Taxi Stand Lane, Mawaiya, Lucknow (U.P.) Phone : /B, R.R. Complex (Near Sundaraiah Park, Adjacent to Manasa Enclave Gate), Bagh Lingampally, Hyderabad (A.P.) Phone : The publishers have taken all possible precautions in publishing this book, yet if any mistake has crept in, the publishers shall not be responsible for the same. This book or any part thereof may not be reproduced in any form by Photographic, Mechanical, or any other method, for any use, without written permission from the Publishers. Only the courts at Agra shall have the jurisdiction for any legal dispute. ISBN : Price : 330/- (Rs. Three Hundred Thirty Only) Code No Printed at : UPKAR PRAKASHAN (Printing Unit) Bye-pass, AGRA

4 Contents Part-I Quantitative Techniques & Data Interpretation Part-II Logical Reasoning Part-III Language Comprehension. { Part-IV General Awareness

5 General Information Eligibility Graduates in any discipline or Final year students of Graduate Courses can apply for CMAT. Pattern of Examination for CMAT Type of Questions Number of Questions Maximum Marks Quantitative Techniques & Data Interpretation Logical Reasoning Language Comprehension General Awareness There shall be negative marking for wrong answers, for each wrong answer 1 mark shall be deducted. Duration of exam will be 180 minutes. At the test venue, each candidate will be seated at a desk with a computer terminal and he/she will be provided with a scratch paper for calculations. After the test, candidate must leave the scratch paper at the desk. Rough work cannot be done on any other paper/sheet, as nothing will be allowed inside the testing room. No breaks will be given during the test.

6 Basic Numeracy & Data Interpretation

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8 1 Indices and Surds Indices If a number a is taken three times and added, then the sum is written as three times a which is written as 3 a 3a. Instead of adding, if a taken three times and multiply, the product is written as cube of a a 3. We say that a is expressed as an exponent. Here, a is called the base and 3 is called the power or index or exponent. Similarly a can be expressed to any exponent n and accordingly written as a n. This is read as a to the power n or a to the power of n or a raised to the power n. For example and Law of Indices 1. a m a n a m + n 2. a m a n 3. (a m ) n a mn 4. a m 1 a m 5. m a a 1/m a m a n a m n 6. (ab) m a m b m 7. a a 1 a Surds Any number of the form p q where p and q are integers and q 0 is called a rational number. Any real number which is not a rational number is an irrational number. Amongst irrational numbers, of particular interest to us are surds. Amongst surds, we will specifically be looking at quadratic surds surds of the type a + b and a + b + c where the terms involve only square roots and not any higher roots. We do not need to go very deep into the area of surds. What is required is a basic understanding of some of the operations on surds. If there is a surd of the form a + b, then a surd of the form a b is called the conjugate of the initial surd. The product of a surd and its conjugate will always be a rational number. Rationalization of surd It is difficult to perform arithmetic operations on it, when there is 1 a surd of the form. Hence, the denominator is converted into a rational number thereby a + b facilitating ease of handling the surd. This process of converting the denominator into a rational number without changing the value of the surd is called rationalization. To convert the denominator of a surd into a rational number, multiply the denominator and the numerator simultaneously with the conjugate of the surd in the denominator so that the denominator gets converted to a rational number without changing the value of the fraction. That is, if there is a surd of the type a + b in the denominator, then both the numerator and the denominator have to multiplied with a surd of the form a b or a surd of the types a + b to convert the denominator into a rational number. Square root of a surd If there exists a square root of a surd of the type a + b, then it will be of the form x + y. We can equate the square of x + y to a + b and thus solve for x and y. Here, one point should be noted. When there is an equation with rational and irrational

9 4P Arithmetic terms, the rational part on the left hand side is equal to the rational part on the right hand side and, the irrational part on the left hand side is equal to the irrational part on the right hand side of the equation. Comparison of surds Sometimes we need to compare two or more surds either to identify the largest one or to arrange the given surds in ascending or descending order. The surds given in such cases will be such that they will be close to each other and hence we will not be able to identify the largest one by taking the approximate square root of each of the terms. In such a case, the surds can both be squared and the common rational part be subtracted. At this stage, normally one will be able to make out the order of the surds. If even at this stage, it is not possible to identify the larger of the two, then the numbers should be squared once more. Example 1. If 32 x, then find the value 3 8 x of x. 32 Sol. x 3 8 x x 4/ x 4/ x x 2 6 x 64 Example 2. Simplify : 2 (a b) k 2 (b c)k (c a) k Sol. 2 (a b) k 2 (b c)k 2 (c a) k 2ak bk + bk ck + ck ak 2 1 Example Sol. Let x 10 x 10x x 2 10x x 2 10x 0 x (x 10) 0 x 0 or x 10 Note x cannot be zero. Example 4. Simplify : (343) 1/3 (625) 1/4 (512) 1/3. Sol. (343) 1/3 (625) 1/4 (512) 1/3 (7 3 ) 1/3 (5 4 ) 1/4 (8 3 ) 1/ Example 5. (64) 4 (125) 2? 3 Sol. (64) 4 (125) 2 (64) 4/3 (125) 2/3 (4) 4 (5) Example 6. ( 3) 5 ( 3) 3 3/2? ( 3) 2 Sol. ( 3) 5 ( 3) 3 ( 3) 2 3/2 (3) [ 5/2 (3) 3/2 ] (3) 1 5 [ 3 ] [ 3 2 ] /2 [3 2 ] 3/ /2 3/2 Example (0 008) 2/3 ( ) Sol (0 008) 2/3 0 ( )? {(0 2)3 } 2/ (0 2) (0 2) ?

10 Arithmetic 5P Example 8. ( 1) ? Sol. ( 1) Example ? Sol Example 10. If what is the value of (b a). Sol. L.H.S a 5 b, then (3) 2 (2 5) Since, L. H. S. R. H. S. Therefore, a 5 b Now, a 9 and b 19 b a Example. 5 5x x 12, then x? Sol. 5 5x x 12 (5) 2 (10x 12) 5 5x x 24 Since the bases are equal on both sides, their powers on both sides must also be equal. 5x x 24 20x 5x x 32 x / /3 Example 12. ( 144) ( 1331) 12 Sol. [() 2 1/ / ] [() ] 12 () () Example 13. (512) 216? 216 Sol. (512) (512) 1 36 (2 9 ) /4 4 2 Exercise 1. If 6 5x x 12, then x? (A) 3 (B) 2 (C) 1 (D) 4 2. (81) 1/4 (125) 2/3 (729) 1/2 (27) 1/3 (625) 3/4? (A) 27 5 (C) (B) 27 5 (D) 21

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