Onlinetest360.com quantitative aptitude PDF

Shashikanth

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INDEX TOPICNAME PageNo. 1. Basic Calculations2-9 2. Number System10-21 3. L.C.M. & H.C.F22-29 4. Percentages 30-38 5. Average 39-48 6. Ratio and Proportion49-59 7. Partnership 50-65 8. Mixtures (or) Alligations66-71 9. 72-81Profit and Loss 10. 82-86Problems on Ages 11. Time and Work87-94 12. Pipes and Cisterns95-101 13. 102-111Time and Distance 14. Problems on Trains112-118 15. Boats and Streams119-124 16. 125-133Simple Interest 17. Compound Interest134-142 18. Clocks 143-148 19. Calendars 149-153 20. 154-164Mensuration - 2D 21. 165-170Mensuration - 3D Key to Assignments171-173 www.onlinetest360.com 1 1. Basic Calculations VBODMAS The order of various operations in exercises involving brackets and functions must be performed strictly according to the order of the letters of the word VBODMAS. Each letter of the word VBODMAS stands as follows: V for Vinculum: -(bar) B for Bracket: [{()}] O for Of: of D for Division: ÷ M for Multiplication: x A for Addition: + S for Subtraction: Note:There are three brackets. 1. ( )2. { }3. [ ] Theyare removed strictly in the order ( ), { } and [ ]. Solved Example: ª ­ª º½º 1 11 1°1 5° « » 1.

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• Publié par: onlinetest360
• Publié le: 22 octobre 2016
• Nombre de lectures: 4
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

INDEX  TOPIC NAME Page No. 1.Basic Calculations 2-9 2.Number System 10-21 3.L.C.M. & H.C.F 22-29 4.Percentages 30-38 5.Average 39-48 6.Ratio and Proportion 49-59 7.Partnership 50-65 8.Mixtures (or) Alligations 66-71 9.72-81Profit and Loss 10.82-86Problems on Ages 11.Time and Work 87-94 12.Pipes and Cisterns 95-101 13.102-111Time and Distance 14.Problems on Trains 112-118 15.Boats and Streams 119-124 16.125-133Simple Interest 17.Compound Interest 134-142 18.Clocks 143-148 19.Calendars 149-153 20.154-164Mensuration - 2D 21.165-170Mensuration - 3D Key to Assignments 171-173

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1. Basic Calculations VBODMAS The order of various operations in exercises involving brackets and functions must be performed strictly according to the order of the letters of the word VBODMAS. Each letter of the word VBODMAS stands as follows: V for Vinculum : - (bar) B for Bracket : [{( )}] O for Of : of D for Division : ÷ M for Multiplication : x A for Addition : + S for Subtraction : - Note:There are three brackets. 1. ( ) 2. { } 3. [ ]  They are removed strictly in the order ( ), { } a nd [ ]. Solved Example:     1 1 1 1  1 5    1.Simplify: 434 of51 1 31    2  4 85 2 3          Sol:niossrexpeenivG      9 1 6 9 1 6  5 5     =  of 1 1 3    2  3 4 85 2            9 1 6 9 1 6   5   =   of1 13     2 5 2 3 8        9  69 1 1 6  1 9   =  of1 1    2 5 2 3 8    9  96 6 9 1 1 6   =  of   2 5 2 3 8   9  16 9 16 69   =      2  3 85 2  9  1 6 1 6 9   =     2 5 2 4 8   9  1 61 0 3 5   =    2 1 2 0   9 1 0 51 5 4 01 0 51  =  = 2 1 2 0 1 2 0 5 1 1  =  1 2 0 Square Root And Cube Root Squareumber.: A number multiplied by itself is known as the square of the given n E.g.square of 3 is 3 x 3 = 9 Square Root: Square root of a given number is that number which when multiplied by itself is equal to the given number. It is denoted by the symbol . 2 E.g.= 4 x 4 = 16square root of 16 is 4 because 4

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 Thus, 16 = 4. Methods of finding the Square Root: I.Prime Factorization Method:This method is used when the given number is a perfect square or when every prime factor of that number is repeated twice. Follow the ste ps as mentioned below. 1.First find the prime factors of the given number. 2.Group the factors in pairs. 3.Take one number from each pair of factors and then multiply them together. This product is the square root of the given number. E.g.Find the square root of 225. Sol: 225 = 5 x 5 x 3 x 3 So, √225 = 5 x 3 = 15. II.Method of Division:This method is used when the number is large and the factors cannot be easily determined. E.g. Find the square root of 180625.

So, the square root of 180625i.e. √180625 is 425. Explanation: 1.First separate the digits of the number into periods of two beginning from the right. The last period may be either single digit or a pair. 2.Find a number (here it is 4) whose square may be equal or less then the first period (here it is 18). 3.Find the remainder (here it is 2) and bring down the next period (here it is 06). 4.Double the quotient (here 4) and write to the left (here 8). 5.The divisor of this stage will be equal to the above sum (here 8) with the quotient of th is stage (here 2) suffixed to it (here 82). 6.Repeat this process till all the periods get exhausted. 7.The final quotient is equal to the square root of the given number (here it is 425). Square root of a Decimal:If the given number is having decimal, separ ate the digits of it into periods of two to the right and left starting from the decimal point and then proceed as followed in the example. E.g.1. Find the square root of 1.498176.

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So,√1.498176 = 1.224 Note: The square root of a decimal cannot found exactly, if it has an odd number of decimal places. Try with finding the square root of 0.1790136 Square Root of a Fraction: Case 1:If the denominator is a perfect square, the square root is found by taking the square root of the numerator and denominator separately. 2 6 0 1 E.g.Find the square root of . 4 9 2 6 0 1 2 6 0 1 5 15 1 5 1 2 Sol:= = = = 7 4 9 7 7 4 9 77 Case 2:If the denominator is not a perfect square, the fraction is converted into decimal and then square root is obtained or the denominator is made perfect square by multiplying and dividing a suitable number and then its squar e root can be determined. 4 6 1 E.g.Find the square root of . 8 4 6 1 4 6 12 9 2 2 3 0.3 6 44 Sol: = = = = 7.5911 (nearly) 8 82 4 1 6 Cube:Cube of a number is obtained by multiplying the number itself thrice. E.g.64 is the cube of 4 as 64 = 4 x 4 x 4. Cube Root:The cube root of a number is that number which when raised to the third power produces the given number, that is the cube root of a numberais the number whose cube is a. 3 a . The cube root ofais written as Methods to find Cube Root: 1.Method of Factorization: a.First write the given number as product of prime factors. b.f each type.Take the product of prime numbers, choosing one out of three o This product gives the cube root of the given number. E.g.Find the cube root of 9261. Sol:9261 = 3 x 3 x 3 x 7 x 7 x 7 3 so, 926137 = 21 2.rs up to 6 Digits:Method to find Cube Roots of Exact Cubes consisting the numbe Before we discuss the actual method it is better to have an overview of the following table. Sl. NoIf the cube ends in …Examplethen Cube root ends in 1 1 1 1 2 2 8 8 3 3 7 27 4 4 4 64 5 5 5 125 6 6 6 216 7 7 3 343

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8 8 2 512 9 9 9 729 10 10 0 1000 The method of finding the cube root of a number up to 6 digits which is actually a cube of some number consisting of 2 digits can be well explained with the help of the following examples. E.g.1. Find the cube root of 19683. Sol:First make groups of 3 digits from the right side. 3 3  19,683 : 19 lies between 2 and 3 , so left digit is 2.  687 ends in 3, so right digit is 7. [See the table.]  Thus, the cube root of 19683 is 27. E.g.2. Find the cube root of 614125. 3 3 614 125 : 614 lies between 8 and 9 , so left digit is 8.  125 ends in 5, so right digit is 5. [See the table.]  Thus, the cube root of 614125 is 85. Brainstorming

1.

2.

3.

4.

5.

6.

7.

8.

9.

Let „a‟ and „b‟ be two integers such that a+ b = 10. Then the greatest value of a x b is ___ 1. 20 2. 100 3. 21 4. 24

If a factory A makes x cars in an hour and another factory B, makes y cars every half an hour, how many cars will both factories make in 4 hours? 1. 4x+4y 2. 4x+8y 3. 8x+4y 4. 4x_2y

Which of the following is the same as 50+12? 1. 10(5+3) 2. (605)+(100252) 3. 12x2

x 1 If x*y = xy- then the value of 6* is _______ y 3 1. 16 2. 17 3. -16

If 4 x 1. 2

3 2 , then the value of x is _______ 2. 3 3. 4

3 x 3 If the 2 x5 = 5x10 , then the value of x is ________ 1. 4 2. 3 3. 2

1 x If 5 = , then the value of x is ________ 2 5 1 1. 2. -2 2

3. 2

5 1 If 7 xy = 17, then the value of (x, y) is ________ x 4 1. (6, 2) 2. (7, 2) 3. (9, 2)

3423 = ? 4323 9 1. 4

3 2. 2

1 1 3. 1 8

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4. 5043

4. -17

4. 5

4. 1

4. -4

4. (8, 2)

7 4. 3 6

5

10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

1 1 of 111  of ? = 0 3 7 3 1. 1 2. 3 3. 9 1 3 Which of the following fraction is greater than but less than ? 2 2 1 9 2 3 2 9 1. 2. 3. 3 9 4 7 5 7 2 2 2 (0.0 1)(0.1 1)(0.0 1 4) = ? 2 2 2 (0.0 0 4)(0.0 1 1)(0.0 0 1 4) 1. 0.01 2. 0.1 3. 100 27 The number 10 -1 is not divisible by ____ 1. 9 2. 90 3. 11 3 2.30.0 2 7 = 2 (2.3)0.6 90.0 9 0 1. 0 2. 2.6 3. 2.3 2y y If 10 = 25 then what is the value of 10 ? 1 1. -5 2. 5 3. 2 5 b 2ab 2 If = 0.25 then what should the value of  ? a 2ab 9 4 5 1. 1 2. 3. 9 9  10.1 0.0  Which number is equal to    0.0 1 0.1   1. 1.01 2. 1.1 3. 10.1 What is the value of [0.3+0.3-0.3-0.3 x (0.3 x 0.30)] 1. 0.09 2. 0.27 3. 0.60 3 3 3 Find the number which is equal to (50) + (-30) + (-20) 1. 3x50x30x(-20) 2. 30x50x3x20 3. 3x50x(-30) Find the value of the following: 111111x11 = _______ 1. 122221 2. 1222221 3. 222221 5776800x11 = ___________ 1. 65344800 2. 63544800 3. 62544800 12369x11 = ________ 1. 135069 2. 136059 3. 136069 15.60x0.30 = ? 1. 4.68 2. 0.458 3. 0.468 3 4 2 0 ?  x7 =? 1 9 0.0 1 3 5 6 3 1 8 1. 2. 3. 9 5 7 If 2276  155 = 79.2, the value of 122.76  15.5 is equal to 1. 7.092 2. 7.92 3. 79.02

20. 21. 22. 23. 24. 25.

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4. 12

3 3 4. 4 9

4. 10

4. 10

4. None of these

4.

1 2 5

4. 2

4. 10.01

4. None of these

4. 3x(-30)x(-20

4. 12222221

4. 63545800

4. 135059

4. 0.0468

4. None of these

4. 79.2

6

0.2 8 9 = ? 0.0 0 1 21 1 7 0 1. 1 1

30.

1 1 3. 6 2 8

27.

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26.

33.

5 1 5 7 8 Which is greater among , , and , 9 1 9 8 9 5 1 5 1. 2. 9 1 9

32.

28.

29.

2 080.5  12 2 0? 1. 8

3 5 If 5 = 2.24, the value of will be __________ 2 50.4 8 1. 0.168 2. 1.68 3. 16.8

1 5 4. 6 2 8

4. 469

3. 496

2 3 13 -12 = ? 1. 369

2 2 (17) +(23) = ? 1. 718

2. 396

4. None of these

7

3. 2

3. 12

1 7.2 8? = 200 3.60.2 1. 120

2. 1.20

5555+6666-9999-1111 = ? 1. 1001 2. 1011

3. 1111

1 7 2. 1 1 0

3. 80

0.1 7 3. 1 1

7 3. 8

2. 818

3. 988

31.

4. 1221

Four of the five parts numbered (1), (2), (3), (4) and (5) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.

8 4. 9

4. 0.12

2. 18

12  0.09 of 0.3x2 = ? 1. 0.80 2. 8.0

1 7 4. 1 1

37.

36.

38.

39.

What should come in place of the question mark (?) in the following equation? 85.147+34.912x6.2+? = 802.293 1. 8230 2. 8500 3. 8410 4. 8600

What approximate value should come in place of the question mark (?) in the following equation? 2 66 % of ? = 32.78x18.44 6 1. 900 2. 880 3. 920 4. 940

35.

1 1 2 1 4 31 38 = ? 2 7 7 4 1 1 1 3 1. 5 2. 5 2 8 2 8

34.

4. None of these

4. 8283

4. 168

What should come in place of question mark (?) in the following equation? 5679+1438-2015 = ? 1. 5192 2. 5012 3. 5102 4. 5002

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

1 1. 40% of 160+ of 240 2. 120% of 1200 3 1 3. 38x12-39x8 4. 6 of 140-2.5x306.4 2 In the following equation what value would come in place of question mark(?)? 5798-? = 7385-4632 1. 3225 2. 2595 3. 2775 4. 3045

What should come in place of question mark (?) in the following equation? 2 197x?+16 = 2620 1. 22 2. 12 3. 14 4. 16

Which of the following numbers are completely divisible by seven? A. 195195 B. 181181 C. 120120 1. only A & B 2. only B & C 3. only D & B

D. 891891 4. All are divisible

what should come in the place of the question mark (?) in the following equation 2 1 9 5 1 0    = ? 2 5 2 0 1 2 1 7 7 7 9 1 1 9 2 9 1. 2. 11 3. 4. 1 1 2 5 1 0 4 5 0 9 0

What should come in the place of the question mark (?) in the following equation? 2 8 ?  ? 1 1 2 1. 70 2. 56 3. 48 4. 64

What should come in the place of the question mark (?) in the following equation? 48 ? +32 ? = 320 1. 16 2. 2 3. 4 4. 32

What should come in the place of the question mark (?) in the following equation? 2 (7? ) 8 1 4 9 1. 9 2. 2 3. 3 4. 4

What should come in the place of the question mark (?) in the following equation? 2 2 4 52 7 . 2 1 3 5 1. 81 2. 1 3. 243 4. 9

Simplify: 18 1 04 +32  (4+10  2-1) = ___________ 1. 5 2. 9 3. 8

Solve: 4-  6  1 2  543   . 1. 5 2. 4

3. 6

If x=4, y=3, then the value of x  yx2  is _________ 7 1 4 1. 2. 1 3. 4 2 5

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4. 7

4. 8

5 4. 4

8

9

 1) 4 16) 1 31) 3 46) 3  2) 2 17) 3 32) 4 47) 1  3) 2 18) 2 33) 2 48) 4  4) 3 19) 2 34) 4 49) 3  5) 2 20) 2 35) 3 50) 3  6) 1 21) 2 36) 1  7) 2 22) 2 37) 2  8) 3 23) 1 38) 3  9) 2 24) 4 39) 2 10) 2 25) 2 40) 4 11) 4 26) 4 41) 2 12) 1 27) 4 42) 4 13) 3 28) 2 43) 4 14) 4 29) 2 44) 2 15) 2 30) 1 45) 1 2. NUMBER SYSTEM Natural Numbers (N):Counting numbers 1, 2, 3, . . . . . are called Natural numbers. They are also called Positive Integers. N = {1, 2, 3, . . . . . . . .} Whole Numbers (W):All the natural numbers including 0 together constitute the set of Whole numbers. W = {0, 1, 2, 3, . . . . . . . .} Integers (I or Z):ng numbers together constitute theAll the whole numbers including negative counti set of Integers. I or Z = {. . . . . . ., -3,-2,-1, 0, 1, 2, 3 . . . . . . . .} p Rational Numbers (Q):Numbers which are in the form of,wherep, qare integers andq≠ 0, are q called Rational numbers. p Q = { ,(q  0)/ p, q  Z} q 1 22 E.g.etc., , -3, 1, 3.2, 3 7 Note: 1.Rational numbers are divided into two groups, namely integ ers and non-integers. 2.Non-integer belonging to the set of rational numbers is called fraction. p Fraction:A number expressed in the form ofis also called fraction, where „p‟ is the numerator and q „q‟ is the denominator. Fraction is apart of an integer. 6 2 1 E.g. ,, , etc. 5 7 6 Proper Fraction:Fractions in which Numerator < Denominator are called Proper Fractions. 1 3 7 E.g. ,, , etc. 5 7 9 Improper Fraction:Fractions in which Numerator > Denominator are called Improper Fractions. E.g.8/3, 7/5, 9/4, etc. Mixed Fraction:It has two parts. One is integer and the other is a fraction. E.g.1 1/3, 2 3/5, 5 4/3, etc. Note: 1.All the mixed fractions can be converted into improper fractions. 2.A rational number can be expressed in the decimal form. 3.The decimal form of a rational number is either recurring or a terminating decimal. E.g.10/3 = 3.3333… (recurring)

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 3/4 = 0.75 (terminating) Irrational Numbers (Q’):A number which cannot be expressed in the form of rational number is called an Irrational number.  For an irrational number, the decimal part is non -recurring and non-terminating. E.g.It is non√2 = 1.414…. -recurring and non-terminating. Even number:An integer divisible by 2 is called an Even number. E.g.2, 4, 6, 8,…….. Odd Number:An integer not divisible by 2 is called an Odd number. E.g.1, 3, 5, 7,……. Prime Numbers:ny number other then 1 and itself are calledNumbers which are not divisible by a Prime numbers. E.g.2, 3, 5, 7,……. Composite Numbers:Except 1, the numbers which are not prime are called Composite numbers E.g.4, 6, 9, 12,…… Co-prime Numbers:Numbers which do not have any common factor other than 1 are called Co-prime numbers. E.g.(4, 15), (9, 22), (12, 29),…… Note: 1.1 is neither prime nor composite. 2.2 is an even prime number. 3.Co-prime numbers can be prime or composite numbers. 4.-prime numbers.Any two prime numbers are always Co 5.Any two consecutive positive integers are always co -primes. Place Value of a Digit in a Numeral: The value of where the digit is in the number, such as units, tens, hundreds, etc. Face Value:Face Value of a number is the number itself. Consider the number 12654: Place Value of 4 = 4 ones = 4, Face Value of 4 = 4 Place Value of 5 = 5 tens = 50, Face Value of 5 = 5 Place Value of 6 = 6 hundreds = 600, Face Value of 6 = 6 Place Value of 2 = 2 thousands = 2000, Face Value of 2 = 2 Place Value of 1 = 1 ten thousands = 10,000, Face Value of 1 = 1 Perfect Numbers:If the sum of the factors of a given number is twice the number, the number is said to be a Perfect number. E.g.Factors of 6 = 1, 2, 3, 6 and 1 + 2 + 3 + 6 = 12 28, 496, etc….are the other examples of perfect numbers. MULTIPLICATION TIPS: n 1.For multiplication of a given number by 9, 99, 999, etc., that is by 10–1, the easy way is: Put as many zeros to the right of the multiplicant as there are nines in the multiplier and from the result subtract the multiplicant and get the answer. E.g.Multiply 2893 by 99. Sol:2893 x 99 = 2893 (100–1) = 289300–2893 = 286407. n 2.+ 1, the easy wayFor multiplication of a given number by 11, 101, 1001, etc., that is by 10 is: Placenzeros to the right of the multiplicant and then add the multiplicant to the number so obtained. E.g.Multiply 3782 by 11. Sol:3782 x 11 = 3782 (10 + 1) = 37820 + 3782 = 41602. 3.Double the multiplier and thenFor multiplication of a given number by 15, 25, 35, etc. multiply the multiplicant by this new number and finally divide the product by 2. E.g.Multiply 5054 x 15 = ½ (5054 x 30) = ½ (151620) = 75810

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4.For multiplication of a given number by 5, 25, 125, 625, etc., that is, by a number which is some power of 5. Place as many zeros to the right of the multiplicant as is the power of 5 in the multiplier, then divide the number so obtained by 2 raised to the same power as is the power of 5. E.g.2982 x 5 = 29820/2 = 14910 2  5739 x 25 = 573900/2 = 143475 p q r a) No. of factors of a given number:If Nabc..... then the number of factors ofN= (p+ 1) (q+ 1) (r+ 1)…………., where a, b, c are prime factors ofNandp,q,r,………. are positive integers. E.g.Find the number of factors of 24. 3 1 Sol:24 = 23  The number of factors of 24 = (3 + 1) (1 + 1) = 8. p q r b) Sum of the factors of a given number:If N   then the sum of the factors ofN= a b c..... p1 q1 r1 a1 b1 c1  .......... ......... where a, b, c are prime factors ofNandp,q,r,………. are a1 b1 c1 positive integers. E.g.Find the sum of the factors of 24. 3 1 Sol:24 = 23 31 11 21 31  Sum of the factors of 24 =  6 0. 21 31 c) No. of ways of expressing a given number as a product of two factors: p q r If Nabc..... where a, b, c are prime factors of N and p, q, r,………. are positive integers then 1 the number of ways in which N can be expressed as product of two factors =  (p1)(q1)(r1).....  . 2 E.g.Find the number of ways of expressing 48 as a product of two factors. 4 1 Sol:48 = 23 1 1 No. of ways =  (p1)(q1)    (41)(11)  5 . 2 2 d) No. of ways of expressing a given number which is a perfect square as a product of two factors: p q r If Nabc ..... where a, b, c are prime factors of N and p, q, r,………. are positive integers then the number of ways in which N can be expressed as product of two factors = 1  (p1)(q1)(r1)........1  . 2 E.g.Find the no. of ways of expressing 36 as a product of two factors. 2 2 Sol:36 = 23 1 1 No. of ways =  (p1)(q1)1    (21)(21)1  5 . 2 2 TIPS ON SQUARES: ConditionMethodExample 2 (35) = To square any 2 {3(3+1)}25= number ending (a5) = {a(a+1)}25 1225 with 5. To square a Count the number of digits in the giv en number and 2 number in (11) = 121, start writing numbers in ascending order from one to 2 which every (111) =12321 this number and then in descending order up to one. digit is one. 2 To square a Use the formula: (1004) =

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