1. Quantitative Aptitude Preparation
Prepared by : Rupal Patel

2. 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

3. 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

4. 8 3 5 2 6 Place of each digit E.g. 83526 Ten Thousand’s Place
Ten Thousand’s Place
Thousand’s Place
Hundred’s Place
Ten’s Place
Unit’s Place

5. 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

6. 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

7. 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

8. 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

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

10. 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………...

11. 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

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

13. 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

14. 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

15. 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.

16. 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.

17. 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

18. 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

19. “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

20. Simplify the following examples
/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

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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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
50C

31. 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

32. 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

33. Thank you