Quantitative Aptitude – Simplification
Simplification is the process of finding the most simplest form of a given expression. In competitive exam simplification is another important topic. At least two or three questions are from simplification. So, now we will discuss the details of simplification here in this page.
An equation may consist few numbers and few arithmetic operators in it. And, we can simplify the equation on the basis of priority of the operators. So, we need to know which operators has most priority and which has less. And, here comes a rule known as BODMAS rule.
As we know that BODMAS rule tells us about the priority of the operators. So, what does BODMAS stands for-
- B = Bracket
- O = Of
- D = Division
- M = Multiplication
- A = Addition
- S = Subtraction
This means, first of all we need to remove brackets from the expression, if any. Brackets should be removed in order of, (), {} and then []. Then we do “Of” operations and so on in the following order.
And, one more important thing is Virnaculum or Bar. If an expression has virnaculam then apply the virnaculam first on the expression. BODMAS rule will be applied on the expression after virnaculam.
Few examples of Simplification
Simplification: Example 1
Simplification of: 16200 / 270 / 30
Answer: If your answer is 1800 then you are wrong. If your answer is 2 then your are right. And, do division from left to right. So, first of all (16200 / 270) = 60. Then divide 60 with 30 and the result will be 2.
Simplification: Example 2
Simplification of: 2540 + (340 / 17)
Answer: According to BODMAS rule, first of all we need to simplify the expression which are within brackets. So, 340 / 17 = 20. Now, add this result with the remaining portion of the expression. 2540 + 20 = 2560 will be the answer.
Simplification: Example 3
A man has some hens and cows. Now, total number of heads be 100 and total number of feet equals 316. So, find the number of hens and cows that man have.
Answer: Let the number of hens be x and the number of cows be y.
x + y = 100 …….. (i)
As hens has two legs and cows has four legs, so, 2x + 4y = 316 or x + 2y = 158 …….. (ii)
Solving (i) and (ii) we get:
x + 2y = 158
x + y = 100
(-)
———————-
y = 58
So, x = (100 – y) = 42
Therefore, the number of hens be 42 and number of cows be 58.
Few Examples to Test your Simplification learnings:
Example #1
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
So, in this example we need to find the simplified value of the expression. And, to do this we need to follow the BODMAS rule.
So, here we see Bracket, Addition, Subtraction, Multiplication and Division. And, according to BODMAS rule we do brackets first then division then multiplication then addition and then subtraction.
Like,
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
or, 10 + [-18 + 2 {-13 + 55 - 21}]
or, 10 + [-18 + 2 {42 - 21}]
and, 10 + [-18 + 2 x 21]
or, 10 + [-18 + 42]
or, 10 + 24
finally, 34
Example #2
1440 / 12 + ? x 10 = 320
1440 / 12 + ? x 10 = 320
So, in this example we need to simplify the expression and find the missing number. And, to do this we need to follow the BODMAS rule.
So, here we see Addition, Subtraction, Multiplication and Division. And, according to BODMAS rule we do division first then multiplication then addition and then subtraction.
Like,
Let, the missing number be A. So,
1440 / 12 + A x 10 = 320
120 + A x 10 = 320
120 + 10A = 320
10A = 320 - 120
10A = 200
A = 200 / 10
A = 20
Example #3
Let, the share of C is X.
Therefore, the share of B is: X/2.
And, the share of A is: 1/4 x X/2 = X/8
Therefore,
X/8 + X/2 + X = 130
(X + 4X + 8X) / 8 = 130
13X/8 = 130
X = (130 x 8) / 13
X = 10 x 8
So, X = 80
Hence, B's share is:
X/2
= 80 / 2
= 40
Example #4
2 + (2 x 2) + 8 - 4
2 + (2 x 2) + 8 - 4
So, in this example we need to find the simplified value of the expression. And, to do this we need to follow the BODMAS rule.
So, here we see Bracket, Addition and Subtraction. And, according to BODMAS rule we do brackets first then addition and subtraction.
Like,
2 + (2 x 2) + 8 - 4
or, 2 + 4 + 8 - 4
or, 6 + 8 - 4
and, 14 - 4
finally, 10
Example #5
? - [34 - {24 - (14 - 4 / 2 x 2)}] = 24
44 - [34 - {24 - (14 - 4 / 2 x ?)}] = 24
So, in this example we need to simplify the expression and find the missing number. And, to do this we need to follow the BODMAS rule.
So, here we see Subtraction, Multiplication and Division and Brackets. And, according to BODMAS rule we do brackets first then division then multiplication and then subtraction.
Like,
Let, the missing number be A. So,
A - [34 - {24 - (14 - 4 / 2 x 2)}] = 24
or, A - [34 - {24 - (14 - 2 x 2)}] = 24
or, A - [34 - {24 - (14 - 4)}] = 24
so, A - [34 - {24 - 10}] = 24
so, A - [34 - 14] = 24
or, A - 20 = 24
or, A = 24 + 20
finally, A = 44
Example #6
2 x 30 / 6 x 2 x 7
2 x 30 / 6 x 2 x 7
So,in this example we need to find the simplified value of the expression. And, to do this we need to follow the BODMAS rule.
So, here we see Multiplication and Division together. And, according to BODMAS rule we do division first and then multiplication.
Like,
2 x 30 / 6 x 2 x 7
or, 2 x 5 x 2 x 7
or, 10 x 2 x 7
and, 20 x 7
finally, 140
Example #7
Working hours for 6 weeks is,
6 days x 8 hours x 6 weeks
= 6 x 8 x 6
= 288 hours.
Suppose, the computer operator works overtime for X hours.
Therefore,
(288 x 50) + (75X) = 16275
75X = 16275 - 14400
75X = 1875
X = 25
So, the computer operator works for,
288 + 25
= 313 hours.
Example #8
Let, the share of Anthony is X
Therefore, the share of Akbar is: 2X/3.
And, the share of Amar is: 1/3 x 2X/3 = 2X/9
Therefore,
2X/9 + 2X/3 + X = 4250
or, (2X + 6X + 9X) / 9 = 4250
or, 17X/9 = 4250
so, X = (4250 x 9) / 17
or, X = 250 x 9
or, X = 2250
Hence, Akbar's share is:
2X/3
or, (2 x 2250) / 3
or, 4500 / 3
finally, 1500
Example #9
Working hours for 7 weeks is,
6 x 10 x 7
= 420 hours.
Suppose, the worker works overtime for X hours.
Therefore,
(420 x 10) + (15X) = 4500
15X = 4500 - 4200
15X = 300
X = 20
So, the worker works for,
420 + 20
= 440 hours.
Example #10
Let, the number of Bulls in the farm is Y.
So, the number of Cows in the farm is 10Y.
Total animals present in the farm is,
10Y + Y
= 11Y
So, the answer must be a multiple of 11.
And, the only option here, which is multiple of 11 is, 44.
So, if you need any farther help on Simplification, then let us know. And, We will discuss on those problems here in www.AptitudeTricks.com. Feel free to ask your questions.