Average

• Average of Given Items :
  
  

Average =		Sum of the given Items
		Number of those Items




• Average Speed :
  
  
  Suppose a Person covers a certain distance at X kmph and an equal distance at Ykmph.
  
  Then, the average speed for the whole journey will be (2XY)/(X+Y) Kmph

✒ Lets do some problems on Average (Click Here)

00:54 - By Unknown 0

 Mathematical Operations

Friends, today we shall discuss another important model of Reasoning Section Mathematical Operations. Of course, even these questions are asked under reasoning section these are mainly dependent on mathematical operations. All calculations will be performed using BODMAS Rule. We can divide these problems in three types.Those are,

1. Symbol Substitution
2. Mathematical Logic
3. Interchange of Signs & Numbers

Now lets discuss these types with detailed examples.

1st Type : Symbol Substitution

In this type, to find the value of the given expression you should replace the symbols by mathematical operations. Then apply the BODMAS Rule (i.e., Brackets, of, Division, Multiplication, Addition, Subtraction).

For the detailed understanding, lets have a look at an example

Example : 42% (9-2) + 6 x 3 - 4

Solution :
42 % (9-2) + 6 x 3 - 4
= 42 % 7 + 6 x 3 - 4
= 6 + 6 x 3 - 4
= 6 + 18 - 4
= 24 - 4 = 20


2nd Type : Mathematical Logic

In this type, they just give you some logical statements followed by some mathematical operations. You should solve the given mathematical operations with the help of given logical statements.

Example : If % stands for greater than, x stands for addition, + stands for division, - stands for equal to, > stands for multiplication, = stands for less than, < stands for minus, then which of the following alternatives is correct ?

1. 3 + 2 < 4 % 6 > 3 x 2 
2. 3 x 2 < 4 % 6 + 3 < 2
3. 3 > 2 < 4 - 6 x 3 x 2 
4. 3 x 2 x 4 = 6 + 3 < 2 

Usually for these type of questions people tend to make direct decisions with the help of given statements. But confusion arises when you tried to  coordinate given mathematical symbols with the logical statements mentioned above. It is because lack of coordination between eyes and brain. So, to avoid confusion you just should make a note of given logical statements in simple mathematical equations format. So that it will be easier for your eye to pick the correct operation.

by using above logical statements, you can use a rough sketch like this,

now you can calculate the values of given operations mentally by picking the right hand side symbols instead of left hand side. Or you just can replace the symbols by taking the reference of above rough sketch.

Solution : Using the symbols correctly as given in the above operations, for the option (2) you will get, 3+2-4>6%3-2. Using BODMAS rule in this inequality, we will get 5-4>2-2 or, 1>0, which is correct.

3rd Type : Interchange of Signs & Numbers

In this type they just give you some random set of numbers and mathematical symbols. And then ask you to choose the correct of symbols to fit the given equation.

Example : Select the correct set of symbols which will fit in the given equation 5  0  3  5  = 20

1. x, x, x
2. =, +, x
3. x, +, x
4. +, -, x

Solution : Using the set of symbols given in options, you will get the Option 2 as the correct answer.

Using the set of symbols given in option 2, you will get the equation,

5-0+3x5 = 20

Using BODMAS rule you will get,

5-0+15=20 or 20-0 = 20 which is correct

Now lets have a look at some examples,

1. '<' means subtraction, '>' means Addition, '+' means Multiplication and '$' means Division. Then what will be the value of 27 > 81 $ 9 < 6 ?

Solution :

27+81%9-6 = 27+9-6 = 36-6 = 30

2. If % means +, - means x, x means -, + means %, then what will be the value of 15 - 2 % 900 + 90 x 100 ?

Solution :

15x2+900%90-100 = 30 + 10 - 100 = -60

3. Q means Addition, J means Multiplication, T means Subtraction, K means Division then what is the value of 30K2Q3J6T5 ?

Solution :

3%2+3x6-5  =  15 + 18 - 5 = 28

4. P means x, R means +, T means %, S means -, then what will be the value of 18T3P9S8R6 ?

Solution :

By substituting the given symbols, you will get the answer 52

5. P means Multiplication, T means Subtraction, M means Addition, B means Division then what will be the value of 28B7P8T6M4 ?

Solution :

28 % 7 x8 - 6 + 4 

= 4 x 8 - 6 + 4 

= 32 - 6 + 4 

= 36 - 6 = 30

Thats all for now friends. In our next post we shall discuss some more problems of Mathematical Operations with higher difficulty level. Happy Reading :)

03:11 - By Unknown 0

 BODMAS

• In The simplifications of numerical questions, the order of mathematical operations to be followed is given in the abbreviated form : "BODMAS", where

• B stands for 'Bracket'
• O stands for 'Of'
• D stands for 'Division'
• M stands for 'Multiplication'
• A stands for 'Addition' and
• S stands for 'Subtraction'.
• Order to be followed by in case of brackets is as follows :
• (   )  : Small Brackets,
• {  } : Curly Brackets   and
• [  ]  : Square Brackets

00:53 - By Unknown 0

 Problems on LCM and HCF

☛ Read Basics of LCM and HCF Here, Before starting Practice 


1. Find the least number which when increased by 4 is exactly divisible by 8, 16, 24, 30 and 32 ?
a)   480
b)   484
c)   476
d)   472
e)   None of these

2. What is the greatest number of five digits which when 3769 is added to it will be exactly divisible by 5, 6 , 10, 12, 15 and 18 ?
a)   4309
b)   99459
c)   100539
d)   99911
e)   None of These

3. Find the minimum number of square tiles required to pave the floor of a room of 2m 50cm long and 1m 50cm broad ?
a)    50
b)   750
c)   45
d)   15
e)   None of these

4. Five bells toll together at the intervals of 5, 6, 8, 12 and 20 seconds respectively. Find the number of times they toll together in one hour's time (Inclusive of the toll at the beginning)
a)   120
b)   31
c)   30
d)   5
e)   None of These

5. A milk man has three different kinds of milk 493liters, 551 liters and 435 liters. Find the minimum number of equal size containers required to store all the milk without mixing.
a)   29
b)   51
c)   58
d)   49
e)    None of these

6. The circumference of the front and back wheels of a vehicle are 6 3/14 m and 8 1/18 m respectively. At any given moment, a chalk mark is put on the point of contact of each wheel with the ground. Find the distance traveled by the vehicle so that both the chalk marks are again on the ground at the same time
a)   217.5 m
b)   435 m
c)    412m
d)   419m
e)   None of these

7. The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 420, the other number is
a)   150
b)   225
c)   180
d)   240
e)   None of these

8. Two persons A and B walk around a circular track whose radius is 1.4 km. A walks at a speed of 176 meters per minute while B walks at a speed of 110 meters per minute. if they both start at the same time, from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again? (in Hours)
a)   6 2/3
b)   2 1/3
c)   5 1/4
d)   3 2/3
e) None of these

9. Find the least number which when divided by 8, 9, 15, 24, 32 and 36 leaves remainders 3, 4, 10, 19, 27 and 31 respectively?
a)   2880
b)   2885
c)   2974
d)   2875
e)   None of these

10. Find the greatest number which when divide 357, 192 and 252 leaves same remainder in each case
a)   45
b)   1
c)   15
d)   Cant be determinde
e)    None of these




Solutions :


1.  LCM of 8, 16, 24, 30 and 32 is 480
     So, Required number is 480 - 4  =  476

2.  LCM of 5, 6, 10, 12 and 18 is 540
      On dividing  (99999 + 3769)  by 540, the remainder is  88
      So, the required number is 99999 - 88 = 99911

3.  HCF of 250 cm and 150 cm is 50 cm, which is the side of the tile

     So, the required number of tiles  =  (250 X 150) / (50X50)  =  15

4.  Time after which all the bells tol together is the LCM of 5, 6, 8, 12 and 20.
       i.e., 120 seconds = 20   minutes
      The number of times they toll together in one hour =  60/2  = 30 + 1 (beginning tone)
         So, the answer is 31

5.  As minimum number of containers are required, the size of the container should be maximum and the size is also equal. so size of the container will be HCF of 493, 551 and 435 i.e., 29
     So, required number of containers is =  (493+551+435) / 29  =  51

6.  The required distance is the LCM of 6 3/14  and 8 1/18
      LCM of 6 3/14 and 8 1/18 =  LCM (87/14, 145/18)
      =>  LCM(87,145) / HCF (14,18)  =  435/2  =  217.5m
7.  LCM =  28 HCF
      LCM + HCF = 1740
       =>  28  HCF + HCF = 1740
        HCF =  1740/29  =  60 and LCM = 28X60
      if a and b are two numbers, then
       LCM of (a & b) X HCF of (a & b) = aXb
      28X60X60 = x X 420  = >  x = 240
         So, the other number is 240


8.   Circumference of the track is 2πr
        = 2 X (22/7) X 1400m = 8800 m


         Time taken by A to complete one round
           =  (8800m) / (176m/min)  =  (8800X60)/(176) =  3000 sec

        Time taken by B to complete one round

          = (8800) / (110m/min)  =  (8800X60) / (110)  =  4800 sec

         Time they meet together at the starting point is LCM of 3000 and 4800 sec

           i.e., 24000 sec   =  6 2/3 hours

            So, they meet at the starting point after 6 2/3 hours

9.   We can observe that the difference between the numbers and their remainders is same 

         i.e., 8-3  =  9-4  =  15-10  =  24-19  =  32-27  =  36-31  =  5

        So, required answer is 

                                                LCM (8, 9, 15, 24, 32, 36) - 5

                    = > 2880 - 5 = 2875

10.   Required answer is 

               HCF (357-192, 192-252, 357-252)

                 = > HCF (165, 60, 105) = 15

00:52 - By Unknown 0

 LCM and HCF

• Factor : A number is said to be a factor of other when it EXACTLY divides the other.
• Ex : 6 and 7 are Factors of 42.
• Multiple : A number is said to be a multiple of another, when it is Exactly divisible by the other
• Ex : 42 is a multiple of 6 and 7

 Please re - read these definitions. So that you can get the difference between Factor and Multiple.

• Prime Number : Prime number is a number which has no factors except itself and Unity.
• Ex  :2, 3, 5, 7, 11, 13, 17 etc are prime numbers
• Composite Number :  Composite number is a number which has other factors besides itself and Unity.
• Ex : 14, 15, 16, 18 etc
• Co-Prime : Two numbers are said to be Co-Prime (Prime-To-Each Other) when they have no common factors except Unity.
• Note : The Co-Primes need not necessarily be Primes.
• 15 and 19 
• 15, 17 and 22          are        Co-Primes
• Common Multiple : A Common Multiple of two or more numbers is a number which is exactly divisible by each of them.
• Ex : 12 is a common multiple of 2, 3, 4 and 6
• Least Common Multiple  (LCM) : The LCM of two or more given numbers is the Least Number which is exactly divisible by each of them.
• Ex  : 
• 20 is the Common Multiple of 2, 4, 5 and 10
• 40 is the Common Multiple of 2, 4, 5 and 10
• 80 is the Common Multiple of 2, 4, 5 and 10,          But
• Here 20 is the Least Common Multiple of 2, 4, 5, and 10
• Highest Common Factor (HCF) : The HCF of two or more numbers is the Greatest Number which divides each of them Exactly.
• It is also Called Greatest Common Divisor (GCD)
• Ex : Find the HCF of 18, 24
• Factors of 18 --> 1, 2, 3, 6, 9, 18
• Factors of 24 --> 1, 2, 3, 4, 6, 8, 12, 24
• Here the Greatest number, which divides them exactly is 6. So 6 is the H.C.F of 18, 24

In the above example they have given very small numbers. So it was easy for us to find the HCF. What if they ask you to find the HCF for 84 and 540 ? Will you write the factors to both of them and then find out the Highest number? If you are planning to do that , please erase that thought from your mind :) Because there are several methods to make the process simple

Methods of finding HCF :  

• HCF by factorization : 
1. Express each of the given number as the product of Prime Factors
2. Choose common factors
3. Find the Product of Lowest Power of these Factors.
• This Product  is the required HCF of the given Numbers

Ex : Find the HCF of 84, 540

If you find this method lil confusing, dont worry. There is another method to find HCF.

• HCF by Method of Division :
• Consider two different numbers. 
• Divide the longer number by the smaller one.
• Now divide the divisor by the reminder.
• Repeat this process of dividing the preceding divisor by the last reminder obtained, till you get the reminder "0"
• The LAST DIVISOR is the HCF of the given TWO numbers

Ex : Find the HCF of 42, 70

Thats it. Now the answer is 14 :)

☛  Check some Practice Problems on LCM and HCF Here    

00:50 - By Unknown 0

 Divisibility Rules

• A number is divisible by 2, when its unit digit is either Even or Zero.
• A number is divisible by 3, wehen the sum of its digits is divisible by 3.
• A number is divisible by 4, when the number formed by the two extreme right end digits is either divisible by 4 or both these digits are zeroes.
• A number is divisible by 5, when its unit digit is either zero or 5.
• A number is divisible by 6, when it is divisible bye 2 as well as 3.
• A number is divisible is by 7, if it passes the following Test...
• Take the last digit in a number.
• Double and subtract the last digit in your number from the rest of the digits.
• Repeat the process for larger numbers.
• Take an Example 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.
• A number is divisible by 8, when the number formed by its three extreme right end digits is divisible by 8 or when these last three digits are Zeros.
• A number is divisible by 9, when the sum of its digits is divisible by 9.
• A number is divisible by 10, when its unit digit is zero.
• A number is divisible by 11, when the difference between the sums of the alternate digits is either zero or divisible by 11.
• A number is divisible by 12, when it is divisible by 3 as well as 4.
• A number is divisible by 13, if sum of 4 times the digit in units place and the number in the remaining part is multiple of 13.
• If the difference of 5 times the digit in units place and the number in the remaining part is 0 or multiple of 17, then the number is divisible by 17.
• If the sum of double the digit in units place of a given number and number in the remaining part is multiple of 19, then the given number is divisible of 19.

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00:49 - By Unknown 0

 Shortcut for Multiplication (Base Number Method Part 2)

We've already discussed about the Shortcut Method (Base Number Method) for doing multiplications. In the earlier post we've discussed doing the multiplication by taking the base as 100 (Click Here to read that). I mean, you can do the multiplication for the numbers nearer to the 100. Then what about the remaining numbers? Well, being the Guide 4 Bank Exams we have solutions for all Banking Problems... So, lets have a look at some more approaches of the Base Number Method so that it will be easier for you to multiply any number with any number :)

Find the product of 117 and 88

117   --->   +17

  88   --->   -12

____         _____

105             -204           Ans : 10296

Here, note that to take care of -204 of the second part, borrowing a 1 from the first part is not sufficient (because the 100 it becomes when it comes to the second part is not numerically greater than -204). So, we should borrow 3 from 105 (leaving 102 as the first part) which becomes 300 in the second part to which -204 should be added giving us 96. Hence, the product of 117 and 88 is 10296.

Find the product of 997 and 983.

Here, both the numbers are close to 1000. So take 1000 as the base number.

997   --->   -3

983   --->   -17

_____         _____

980             +51              Ans : 980051

The Second part 51 has only two digits whereas the base 1000 has three zeroes. So, 51 will be written as 051. hence the Product is 980051.

Find the product of 297 and 292.

Here, the numbers are not close to any power of 10 but are close to 300 which is a multiple of 100 which itself is a power of 10. So we adopt 300 as a "temporary base". This temporary base is a multiple (or a sub-multiple) of the main base 100. Here, the temporary base 300 = 3 X 100. Then, the procedure of finding out the deviation from the base, getting the cross-totals and the product of the deviations should be done in a manner similar to the previous cases except that the deviations will be taken from the temporary base.

297   --->      -3

292   --->      -8

____           ____

289              +24            Ans : 86724

We've got the first part of the answer as 289 and the second part of the answer as 24. But before we put these two parts together to get the final result, one more step is involved. The first part of the answer is not the final figure. This is an intermediate stage of the first part. This first part should be multiplied by the same figure with which the power of 10 is multiplied to get the temporary base. In this case, we multiplied 100 (which is the power of 10) by 3 to get the temporary base 300. So, the intermediate stage figure of the first part (289) will also have to be multiplied by 3 to get the final figure for the first part. Hence the first part wil be 867 ( = 3 x 289). Now putting the first and the second parts together , the product of 297 and 292 is 86724 (here remember that the product of the deviations should still have as many digits as the number of zeroes in the base, in the above case it is TWO. because 100 has TWO zeroes).

Thats all for now friends. Tomorrow we shall discuss another Shortcut Method. Happy Reading :)

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00:47 - By Unknown 0