Quantitative Aptitude Preparation Prepared by : Rupal Patel

TOPICS Numbers HCF and LCM Simplifications Square roots and cube roots Problems on numbers Surds and Indices Ratio and Proportion Chain Rule Time and Work Pipes and Cistern Permutations and Combinations

Hindu Arabic Number System We have total 10 digits in Hindu Arabic System. Namely, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Number is a group of digits called numerals. E.g. 83526

8 3 5 2 6 Place of each digit E.g. 83526 Ten Thousand’s Place 8 3 5 2 6 Ten Thousand’s Place Thousand’s Place Hundred’s Place Ten’s Place Unit’s Place

How many zeros? In 1 Thousand? 3 Zeros In 10 Thousand? 4 Zeros In 1 Lakh? 5 Zeros In 1 Crore? 7 Zeros In 10 Crore? 8 Zeros

Write the given numbers in words 9,04,06,002 Nine crore four lakh six thousand two 1,60,05,014 One crore sixty lakh five thousand fourteen 5,04,080 Five lakh four thousand eighty 2,07,09,207 Two crore seven lakh nine thousand two hundred seven

Write the given numbers in figures Six lakh thirty-eight thousand five hundred forty-nine 6,38,549 Twenty-three lakh eighty thousand nine hundred seventeen 23,80,917 Eight crore fifty-four lakh sixteen thousand eight 8,54,16,008 Four lakh four thousand forty 4,04,040

Face Value and Place Value The face value of a digit in a numeral is its own value at whatever place it may be E.g. 6872 Face value of 6 is 6 Face value of 8 is 8 Face value of 7 is 7 Face value of 2 is 2 Place value of 6 is 6000 Place value of 8 is 800 Place value of 7 is 70 Place value of 2 is 2

Examples: Face Value and Place Value The difference between the place value and the face value of 6 in numeral 856973 is 973 6973 5994 None of these The difference between the place value of two seven’s in the numeral 69758472 is 75142 64851 5149 699930

Even and odd numbers A number which is divisible by 2 is called even number. E.g. 0, 2, 4, 6, 8, 10, 12……….. A number which is not divisible by 2 is called odd number. E.g. 1, 3, 5, 7, 9, 11, 13………...

Prime numbers A number which is divisible by only two factors itself 1 is called a prime number. E.g. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Simplifications 35+15*1.5 = ? 75 -84*29+365 = ? 2436 51.5 57.5 5.25 2801 -2801 -2071

HCF – Highest Common Factor LCM – Least Common Multiple HCF and LCM HCF – Highest Common Factor LCM – Least Common Multiple E.g. H.C.F of 36 and 84 is 36 = 6 * 6 = 2 * 3 * 2 * 3 = 22 * 32 84 = 12 * 7 = 2 * 2 * 3 * 7 = 22 * 3 * 7 HCF = 22 * 3 = 4 * 3 = 12 Find the HCF of 15, 25 and 75. 15 = 3 * 5 25 = 5 * 5 = 52 75 = 3 * 5 * 5 = 3 * 52 HCF = 5

HCF and LCM E.g. L.C.M of 16, 24, 36 16 = 2 * 2 * 2 * 2 = 24 24 = 2 * 2 * 2 * 3 = 23 * 3 36 = 2 * 2 * 3 * 3 = 22 * 32 LCM = 24 * 32 = 144 Find the LCM of 22, 54 22 = 2 * 11 54 = 2 * 3 * 3 * 3 = 2 * 33 LCM = 2 * 33 * 11 = 594

So, the lights will again change simultaneously after every 432 sec. Examples The traffic lights at three different road crossings change after every 48 sec., 72 sec. and 108 sec. respectively. If they all change simultaneously at 8 : 20 : 00 hours, then at what time will they again change simultaneously? Ans. LCM of (48, 72, 108) = 432 sec So, the lights will again change simultaneously after every 432 sec. That is = 7 min and 12 sec. Next simultaneous change will take place at 8 : 27 : 12 hours.

Examples The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is. Ans. HCF of (1001, 910) = 91 So, 91 students will get the same number of pens and same number of pencils.

Exercise One bell rings at an interval of 30 minutes and another at an interval of 25 minutes. If they both ring together at 10:00 am, the time when they will next ring together is 12:30 am 10:55 am 12:30 pm 11:30 pm

Exercise What is the least number of students in a class, if they can be made to stand in rows of 8, 12, or 14 each? 158 168 148 178

“BDMAS” rule is used to decide the priority of operations. Simplifications “BDMAS” rule is used to decide the priority of operations. B stands for Brackets D stands for Division M stands for Multiplication A stands for Addition S stands for Subtraction

Simplify the following examples 5005-5000/10 = ? 4505 100+50*2 = ? 200 2-[2-{2-2(2+2)}] = ? -6 The sum of two integers is 25. One integer is 11. Find the other integer. 14 A number divided by 2 is 5 less than that number. What is that number? 10

Simplify the following examples Two pens and three pencils cost Rs. 86. Four pens and a pencil cost Rs. 112. Find the cost of a pen and that of a pencil. pen=25 Rs. Pencil= 12 Rs.

Simplify the following examples In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers. 15 A class starts at 10 a.m. and lasts till 1:27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is : 48 minutes

Simplify the following examples A long yard 225 meters long, 26 trees are planted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees? 9 meters

Square roots and cube roots Evaluate √6084 = ? 78 Find the cube root of 2744. 14 If x*y=x+y+ √xy, the value of 6*24 is : 42 If y=5, then what is the value of 10y √y3 – y2 50 √ 2 100 200 √ 5 500

Problems on numbers Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number. 5 The sum of a rational number and its reciprocal is 13/6. Find the number. 2/3 or 3/2 The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers. x=28 and y=17 The difference between two digit number and the number obtained by interchanging the two digits is 36. What is the difference between the two digits of that number? 4

Ratio and Proportion and chain rule If A:B = 5:7 and B:C = 6:11, then A:B:C is 30:42:77 If 15 toys cost Rs. 234, what do 35 toys cost? 546 Rs. If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it? 60 hours 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? 24 days

If 20 men can build a wall 56 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days? 49 meters If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day? 15 days

Time and work A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work? 6 days A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? Approximately 6.4 days

PIPES and cisterns Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? 20 hours Two pipes can fill a tank in 10 hours and 12 hours respectively while third pipe empties the full tank in 20 hours. If all the three pipes operates simultaneously, in how much time will the tank be filled. 7 hours and 30 minutes

Permutations and combinations n! = n*(n-1)*(n-2)*…..*3*2*1 Permutations = Different Arrangements nPr = n! / (n-r)! Combinations = Different groups or selections nCr = n! / r!(n-r)! Some Examples:- 30! / 28! 870 60P3 205320 100C98 4950 50C50 1

Permutations and combinations How many words can be formed by using all letters of the word “BIHAR” 120 words How many words can be formed by using all the letters of the word “DAUGHTER” so that the vowels always come together? 4320 ways In How many ways a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies. 200 ways In how many ways can the letters of the word “Apple” be arranged? 60 ways

Permutations and combinations A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw? 64 Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? 25200 ways

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