Mathematical Operation

Mathematical Operations - Short-cut Tricks And Examples

In such type of questions some relationships are shown with the help of certain symbols/notations and/ or mathematical signs. Each symbol or sign is defined clearly in the question statement itself. In other words, each symbol or sign is accorded two values –one real value and another assigned value of each symbol or sign and then solve the questions accordingly.

For example, Suppose the triangle (∆) means addition.

We know that triangle is a plane figure but here it has been assigned the value of addition (+).

Thus, 3 ∆ 5 ⇒ 3 + 5 = 8

In this way, two work out such questions substitute the assigned/ implied meanings of the symbol or sign and proceed accordingly.

How to Solve the questions

To solve this type of questions, substitute the real signs in the given expression and then solve the expression according to the BODMAS rule.
Order of Operations – BODMAS

1. 1st. B – Brackets, do all the maths contained in brackets first
2. 2nd. O – Orders, square roots, powers and anything else not listed
3. 3rd. D – Division, do your divisions now
4. 4th. M – Multiplication
5. 5th. A – Addition
6. 6th. S – Subtraction

Example: If + means ÷, × means –, ÷ means × and – means +, then, 8 + 6 × 4 ÷ 3 – 4 = ?

1. – 12
2. – 20/3
3. 12
4. 20/3

Solution. (3): Using the given symbols, we have:

Given expression: = 8 ÷ 6 – 4 × 3 + 4 = 4/3 – 4 × 3 + 4

= 4/3 – 12 + 4 = -20/3.

Type 1: Value of the Given Expression

Example 1: If ‘÷’ means ‘+’, ‘–’ means ‘÷’, ‘×’ means ‘–’ and ‘+’ means ‘×’ then, 62 ÷ 8 – 4 × 12 + 4 = ?

1. 16
2. 26
3. 1/16
4. 6

Solution: (1) Given expression, 62 ÷ 8 – 4 × 12 + 4 = ?

According to question, after replacement of mathematical sign

62 + 8 ÷ 4 – 12 × 4 = ?

= 64 – 48 = 16

Hence, ? ⇒ 16

Type 2: Identification of Correct Equation

Example 2: If ‘–’ means ‘+’, ‘+’ means ‘–’, ‘×’ means ‘÷’ and ‘÷’ means ‘×’; then which of the given equations is correct?

1. 30 + 5 – 4 ÷ 10 × 5 = 58
2. 30 + 5 ÷ 4 – 10 × 5 = 22
3. 30 – 5 + 4 ÷ 10 × 5 = 62
4. 30 × 5 – 4 ÷ 10 + 5 = 41

Solution. (4): From option 4:

30 × 5 – 4 ÷ 10 + 5 = 41

According to question, after replacement of mathematical sign

30 ÷ 5 + 4 × 10 – 5 = 41 = 6 + 40 – 5 = 41 = 46 – 5 = 41

Hence option (4) is correct.

Solved Examples

Example 1: If ‘M’ means ‘÷’, R means ‘+’,  T means ‘-’, and ‘K’ means ‘×’ then what will be the value of the following expression?

20 R 16 K 5 M 10 T8 = ?

1. 36
2. 20
3. 36.5
4. 12

Solution. (2): ? = 20 + 16 × 5 ÷ 10 – 8

or  ? = 20 + 16 ×5/10– 8

or  ? = 20 + 8 – 8 = 20

Example 2: Of the two subjects offered to a class in their final year, 32 students in all are studying Psychology while a total of 26 students are studying Sociology. If 16 students have opted to specialize in both, what is the strength of the class?

1. 74
2. 58
3. 42
4. Date inadequate

Solution. (3): Venn diagram of given information would be as follows.

Total strength of the class = 16 + 16 + 10 = 42

Example 3: How many numbers would remain if the numbers which are divisible by 2 and also those having ‘2’ as only one of the digits are dropped from numbers 1 to 30?

1. 14
2. 17
3. 15
4. 10

Solution. (4):

 

 

Ranking And Ordering

Ranking And Ordering - Short-cut Tricks And Examples

The position of a thing/person etc. in a definite order is called as ‘Rank’.

In this type of test, relative position or rank of some person or object are given and candidates are required to find the rank or position of other person or object.

Type of Questions

Type 1. Rank of a person in a queue

Position of person from upward	= [Total no. of persons – position of person from down] + 1.
Position of person from downward	= [Total no. of persons – position of person from up] + 1.
Position of person from right	= [Total no. of persons – position of person from left] + 1.
Position of person from left	= [Total no. of persons – position of person from right] + 1.

Example 1: Anita ranks twelfth in a class of forty six. What will be her rank from the last?

1. 34th
2. 35th
3. 36th
4. 37th

Solution. (2): Rank of Anita from the last

= [Total students – her rank from first] + 1

= (46 – 12) + 1 = 35th.

Example 2: Ravi is 7 ranks ahead of Sumit in a class of 39. If Sumit’s rank is 17th from the last, what is Ravi’s rank from the start?

1. 14th
2. 15th
3. 16th
4. 17th

Solution. (c): Rank of Ravi from the last = 17 + 7 = 24th.

∴  Rank of Ravi from the start = (39 – 24) + 1 = 16th.

Type 2. Total number of person in a queue

Total no. of persons = [Position of person from upward/right + Position of person from downward/left] – 1.

Example 3: Rakesh ranks 7th from the top and 28th from the bottom in a class. How many students are there in the class?

1. 34
2. 35
3. 36
4. 37

Solution. (1): Total no. of students = [7 + 28] – 1 = 34.

Type 3. When two persons change their rank in a queue

If two persons are on a definite position from up and down (or left and right) and they interchange their ranks, then Total no. of persons in order = [present position of first person + previous position of second person] – 1

Example 4: In a row of girls, Shilpa is eighth from the left and Reena is seventeenth from the right. If they interchange their positions, Shilpa becomes fourteenth from the left. How many girls are there in the row?

1. 34
2. 35
3. 30
4. 37

Solution. (3): Total no. of girls

= [present position of Shilpa + previous position of Reena] – 1

= (14 + 17) – 1 = 30

Previous position of first person or present position of second person = Difference of two positions of second person + previous position of second person = Difference of two positions of first person + previous position of second person.

Example 5: In a row of children, Dipa is fifth from the left and Vijay is sixth from the right. When they interchange their places among themselves, Dipa becomes thirteenth from the left. Then, what will be Vijay’s position from the right ?

1. 4th
2. 14th
3. 8th
4. 12th

Solution. (b): Present position of Vijay

= Difference of two positions of Dipa + previous position of Vijay

= (13 – 5) + 6 = 14th

Solved Examples

Question 1. Aruna ranks twelfth in a class of fortysix. What will be her rank from the last?

Solution: Rank of Aruna from the last

= [Total student – her rank from first] + 1 = (46 – 12) + 1 = 35th.

Question 2. In a class of 35 students Kiran is placed 7th from the bottom whereas Sohan is placed 9th from the top. Mohan is placed exactly in between the two. What is Kiran’s position from Mohan ?

Solution: Position of Kiran from the top = [35 – 7] + 1 = 29 th

Position of Sohan from the top = 9th.

Difference of their positions = 29 – 9 = 20

∴ Mohan’s position from top = 9 + 10 = 19th

Hence, Kiran’s position from Mohan = 29 – 19 = 10th

Question 3. Sonal ranks 7th from the top and 28th from the bottom in a class. How many students are there in the class?

Solution: Total no. of students = [7 + 28] – 1 = 34.

Question 4. There are thirty five students in a class. Suman ranks third among the girls in the class. Amit ranks 5th among the boys in the class. Suman is one rank below Amit in the class. No two students hold the same rank in the class. What is Amit’s rank in the class?

Solution: Suman is one rank below Amit in the class. Hence two girls and four boys are ahead of Amit. Hence Amit’s rank in the class is 7th.

Question 5. Manish ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?

Solution: Total no. of students = [(16 + 29) – 1] + 6 + 5 = 55.

Question 6. In a sequence of children, Kashish is fifth from the left and Mona is sixth from the right. When they interchange their places among themselves, Kashish becomes thirteenth from the left. Then, what will be Mona’s position from the right?

Solution: Second position of Mona = Difference of two positions of Kashish + First position of Mona = (13 – 5) + 6 = 14th

Question 7. Mohan is older than Prabir, Suresh is younger than Prabir. Mihir is older than Suresh but younger than Prabir. Who among the four is the youngest?

Solution:

• Mohan > Prabir > Suresh
• Prabir > Mihir > Suresh

Hence, Mohan > Prabir > Mihir > Suresh