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1 General Aptitude (Numerical Ability) & (Verbal Ability) By
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3 Contents Contents Numerical Ability Chapters Page No. #1. Numbers and Algebra 1-33 Theory + Examples 1-22 Assigment Questions Answer Keys & Explanations #2. Percentage Theory + Examples Assignment Questions Answer Keys & Explanations #3. Time and Work Theory + Examples Assignment Questions Answer Keys & Explanations #4. Ratio, Proportion and mixtures Theory + Examples Assignment Questions Answer Keys & Explanations #5. Permutations and combinations & Probability Theory + Examples Assignment Questions Answer Keys & Explanations #6. Data Sufficiency Theory 107 Assignment Questions Answer Keys & Explanations #7. Reasoning Theory 118 Assignment Questions Answer Keys & Explanations : , info@thegateacademy.com Copyright reserved.web: i
4 Contents #8. Miscellaneous Theory 135 Assignment Questions Answer Keys & Explanations Module Test Test Questions Answer Keys & Explanations : , Copyright reserved.web: ii
5 Contents Contents Verbal Ability Chapters Page No. #1. Vocabulary Based Synonyms and Antonyms 1 6 Theory + Examples 1 Assignment Questions 2 4 Answer Keys & Explanations 5 6 #2. Odd Man Out 7 11 Theory + Examples 7 Assignment Questions 7 9 Answer Keys & Explanations 9 11 #3. Analogies Theory + Examples 12 Assignment Questions Answer Keys & Explanations #4. Multiple Usage Theory + Examples Assignment Questions Answer Keys & Explanations #5. Grammar Brush-Up Theory + Examples #6. Fill in the Blanks Theory + Examples Assignment Questions Answer Keys & Explanations #7. Sentence Correction Theory + Examples 50 Assignment Questions Answer Keys & Explanations : , info@thegateacademy.com Copyright reserved. Web: i
6 Contents #8. Jumbled Paragraphs Theory + Examples Assignment Questions Answer Keys & Explanations #9. Reading Comprehension Theory 75 Assignment Questions Answer Keys & Explanations Module Test Test Questions Answer Keys & Explanations Appendix High Frequency Words and their Meanings : , info@thegateacademy.com Copyright reserved. Web: ii
7 General Aptitude Numerical Ability By
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9 CHAPTER 1 In order to succeed, your desire for success should be greater than your fear of failure..bill Cosby Numbers and Algebra Numbers and Algebra are some of the most favourite topics of the examiners in any exam. Not only there is a large variety of questions that can be framed here, but also it provides the opportunity to test the problem solving skills of the students. We have segregated numbers into various subtopics which we ll be looking at one by one. Numbers Introduction Natural Numbers: All positive integers are natural numbers. Ex: 1, 2, 3, 4, 5,... There are infinite natural numbers and 1 is the least natural number. Based on divisibility there would be two types of natural numbers. They are Prime and Composite. Prime Number: A natural number larger than unity is a prime number if it does not have other divisors except for itself and unity. Note:-Unity (i.e 1) is not a prime number. Procedure to Check a Number is Prime or Not 1. Take the square root of the number. 2. Round off the square root to the next highest integer and call this number as z. 3. Check for divisibility of the number N by all prime numbers below z. If there is no prime number below the value of z which divides N then the number N will be prime. Example: IS 241 is prime or not? 241 lies between 15 and 16.Hence take the value of Z=16. Prime numbers less than 16 are 2, 3, 5, 7, 11 and is not divisible by any of these. Hence we can conclude that 241 is a prime number. Composite Numbers: The numbers which are not prime are known as composite numbers. Note: 1 is neither prime nor composite Co-Primes: Two numbers a and b are said to be co-primes, if their H.C.F is 1. Example (2,3),(4,5),(7,9),(8,11)... : , info@thegateacademy.com Copyright reserved. Web: 1
10 Numbers and Algebra Tests for Divisibility 1. A number is divisible by 2, when its unit digit is even or A number is divisible by 3, when the sum of its digits is divisible by A number is divisible by 4 when the number formed by the last two digits on right hand side is divisible by 4, or if the last two digits are zeros. 4. A number is divisible by 5, when its unit digit is 5 or A number is divisible by 6, when it is divisible by 2 and 3 both. 6. Divisibility test of 7 Method 1: If the digits a, b, c, d of a four-digit number abcd are such that 2b + 3c + d a is divisible by 7, then the original number is divisible by 7 e.g., 1981 = = 42 which is divisible by 7. Hence, 1981 is divisible by 7. Method 2: A number is divisible by 7 if the sum of the product of the digits of the number from left to right with 1, 2, 3, 1, 2, 3, successively is divisible by 7 or is 0. e.g., 392 The required sum = = 21 which is divisible by 7. Hence, 392 is divisible by 7. Method 3: An integer I is divisible by 7, if the difference of the number of its thousands and the remainder of its division by thousand is divisible by 7. e.g., Difference = = 252 which is divisible by 7. Hence, is divisible by 7. Method 4: Any number is divisible by 7, if the number of tens added to five times the number of units is divisible by 7. e.g., 308 Number of tens = 30 The required sum = = 70 which is divisible by 7. Hence, 308 is divisible by 7. Method 5: Any number is divisible by 7, if the number of tens added to ( 2) times the number of units is divisible by 7. e.g., 6727 Number of tens = 672 ( 2) times the number of units = = 658 Number of tens = 65 ( 2) times the number of units = = 49 which is divisible by 7. Hence, 6727 is divisible by 7. : , info@thegateacademy.com Copyright reserved. Web: 2
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