Dear Aspirants,
Welcome to D2G’s Quantitative Aptitude Section. In Clerk Exam most of the questions will be based on simplification. Though easy to do but it is calculative. Once we learn concepts and start solving questions, simplification is nothing. Simplification in bank exams mostly deals with Addition, Subtraction, Multiplication, Division, Square and Cube roots. If we are strong in these things its so simple to do problems based on this.
Basics Concepts and Formulas:-
Squares and Cubes:-
Multiplication Tricks:-
By 5:-
1) To find the multiplication of a number when it is multiplied by 5
Step 1:- Divide the given number by 2
Step 2:- Add one zero ‘0’ at the end
For example,
42× 5
42/2 = 21
Add ‘0’ at the end.
210 is the answer
By 25:-
2) To find the multiplication of a number when it is multiplied by 25
Step 1:- Divide the given number by 4
Step 2:- Add two zero’s ’00’ at the end
For example,
44 ×25
44/4 = 11
Add ’00’ at the end.
1100 is the answer
By 11:-
3) To find the multiplication of a number when it is multiplied by 11
Step 1:- Count the number of digits and write those two numbers at the end leaving a gap to fill the middle terms.
Step 2:- Add the end digits and fill in the middle
Step 3:- We should add the numbers from right to left. If we get a carry while adding add it like as we do in normal addition problems.
For example,
1) 53× 11 = 5_3(Hence here 53 is a two digit number. Subtract the given number by 1 to fill the number of gaps)
Now 3+5 = 8
Put this 8 in the middle
So 583 is the answer.
2) 12345 ×11 = 1_ _ _ _ 5(Here it is a 5 digit number so 5-1 = 4 gaps)
5+4=9
4+3=7
3+2=5
2+1=3
Fill these numbers from right to left.
Here we get, 135795
3) 9527136× 11
Well, we know that 6 will be the last number in the answer. So the answer now is
???????6.
Calculate the tens place: 6+3=9, so now we know that the product has the form
??????96.
3+1=4, so now we know that the product has the form
?????496.
1+7=8, so
????8496.
7+2=9, so
???98496.
2+5=7, so
??798496.
5+9=14.
Here’s where carrying digits comes in: we fill in the hundred thousands place with the ones digit of the sum 5+9, and our product has the form
?4798496.
We will carry the extra 10 over to the next (and final) place.
9+0=9, but we need to add the one carried from the previous sum: 9+0+1=10.
So the product is 104798496.
By 9:-
4) To find the multiplication of a number when it is multiplied by 9
Step 1:- Take the number Subtract 1 from it.
Step 2:- Subtract digit by digit from 9.
Step 3:- While Subtracting last digit from 9 add ‘1’ to it
For example,
1) 53× 99
53-1 = 52
9-5=4
9-3+1=7
So 5247 is the answer
2) 1234× 9999
1234-1=1233
9-1=8
9-2=7
9-3=6
9-4+1=6
So the answer is 12338766
Another method for multiplying by 9:-
8× 9 = 8× 10 – 8 = 72
Similarly 46× 9 = 46 ×10 -46 = 414
One more,
68 ×9 = 68× 10 – 68 = 612
Multiply by 99 or 999 is similar
46× 99 = 46 ×100 – 46 = 4554
38× 999 = 38 ×1000 – 38 = 37962
Square root and Cube root:-
1) How to find a SQUARE ROOT of number.
729
Step1 : First pair the numbers in group from right.
_ __
7 84
Step2: Now to find the ten’s place digit ,find the nearest square to the first grouped pair from left and put the square root of the square.
nearest square of 7 is 4
√4 = 2
Step3: Now to get the unit’s place digit .
Note
If no. ends in Unit’s place digit of the square root
1 1 or 9
4 2 or 8
6 4 or 6
9 3 or 7
5 5
0 0
Therefore the unit digit will be either 1 or 9.
Step4: Now multiply the ten’s place digit .i.e. found in step 1 with its consecutive number and compare the result obtained with the first pair of the original number from left.
Now ,if:
1. If the first pair of the original number > Result obtained on multiplication than select the greater number out of the two numbers as the unit place of the square root.
2.If the first pair of the original number < Result obtained on multiplication ,then select the lesser number out of the two numbers. 2 x 3 =6 7> 6
Therefore for the answer will be 29 .
2) How to find a CUBE ROOT of number.
13824
Step1: Now to find the unit place of the cube root always remember the following points
1.If the Last digit of a cube root is 8 than the unit digit will be 2.
2.If the Last digit of a cube root is 2 than the unit digit will be 8.
3.If the Last digit of a cube root is 3 than the unit digit will be 7.
4.If the Last digit of a cube root is 7 than the unit digit will be 3.
5.If the Last digit of a cube root is other than 2,3,7,8 than put the same number as the unit digit.
Now the unit digit will be 4
Step2: Now strike the last 3 digits of the given number.
13824
Step3: Now find the nearest square of the first 2 digit from the left
Now the nearest cube is 8
Step4: Now 8 is the cube root of 2
Therefore the ten’s place digit is 2
So the answer will be 24
What is BODMAS Rule?
BODMAS rule defines the correct sequence in which operations are to be performed in a given mathematical expression to find its value.
In BODMAS,
B = Bracket
O = Order (Powers, Square Roots, etc.)
DM = Division and Multiplication (left-to-right)
AS = Addition and Subtraction (left-to-right)
This means, to simplify an expression, the following order must be followed.
Do operations in Brackets first, strictly in the order (), {} and []
Evaluate exponents (Powers, Roots, etc.)
Perform division and multiplication, working from left to right. (division and multiplication rank equally and done left to right).
Perform addition and subtraction, working from left to right. (addition and subtraction rank equally and done left to right).
In India, the term BODMAS is used whereas in USA the acronym PEMDAS is used. The full form of PEMDAS is “Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction”. Both are correct and only difference is that these are used in different parts of the world. Some other variations which are used across the world to represent the same concept are BIDMAS, ERDMAS, PERDMAS and BPODMAS.
Examples:-
12 + 22 ÷ 11 × (18 ÷ 3)2 – 10
= 12 + 22 ÷ 11 × 62 – 10 (∵ Brackets first)
= 12 + 22 ÷ 11 × 36 – 10 (∵ exponents)
= 12 + 2 × 36 – 10 = 12 + 72 – 10 (∵ division and multiplication, left to right)
= 84 – 10 = 74 (∵ Addition and Subtraction, left to right)
4 + 10 – 3 × 6 / 3 + 4
= 4 + 10 – 18/3 + 4 = 4 + 10 – 6 + 4 (∵ division and multiplication, left to right)
= 14 – 6 + 4 = 8 + 4 = 12 (∵ Addition and Subtraction, left to right)
Happy Reading!! In our next post we will provide you questions based on Simplification.
