Logical 14 - Mathematical Operations

Practice Questions:

Question 1:

If ‘+’ means ‘–’, ‘–’ means ‘/’, ‘/’ means ‘*’, and ‘*’ means ‘+’ then which of the following will be the value of the expression?

32 + 8 / 2 – 3 * 4

Putting the changed signs, the expression can be rewritten as 32 – 8 / 2 * 3 + 4

Using BODMAS rule, we have

= 32 – 4 * 3 + 4

= 32 – 12 + 4 = 24

The value of the expression 32 + 8 / 2 – 3 * 4 is 24.

Question 2:

Which of the following changes would make the given expression correct?

4 + 4 / 4 – 4 * 4 = 4

(a) ‘+’ and ‘/’ 

(b) ‘–’ and ‘*’

(c) ‘+’ and ‘*’ 

(d) both ‘b’ and ‘c’

By making inter-changes given in ‘a’ we get the expression as:

= 4 / 4 + 4 - 4 * 4

= 1 + 4 - 16

= 5 - 16

= -11

(a) is false

By making inter-changes given in ‘b’ we get the expression as:

= 4 + 4 / 4 * 4 - 4

= 4 + 1 * 4 - 4

= 4 + 4 - 4

= 4

(b) is true

By making inter-changes given in ‘c’ we get the expression as:

= 4 * 4 / 4 - 4 + 4

= 4 * 1 - 4 + 4

= 4 - 4 + 4

= 4

(c) is true

Hence, the answer is (d).

Question 3:

If

12 + 2 = 6

27 + 9 = 3

and 15 + 5 = 3

It is clear that + means / here as 12/2 = 6; 27/9 = 3; 15/5 = 3.

Question 4:

Calculate the value of 182 + 13

182 / 13 = 14

Question 5:

Calculate the value of 50 + [50 + 10]

= 50 / (50 / 10)

= 50 / 5

= 10

Question 6:

Calculate (10 + (6 + (3 + (2 + 1))))

= 10 / ( 6 / ( 3 / ( 2 / 1 ) ) ) 

= 10 / (6 / ( 3 / 2 ) )

= 10 / ( 6 / 1.5)

= 10 / 4

= 2.5

If

aAb implies a + b

aMb implies a – b

aPb implies a * b

aQb implies a / b

Question 7:

Which of the following equations is correct?

(a) 30Q10A4P2M2 = 15

(b) 5P2A4Q2P2 = 14

(c) 2Q3B5P6A7 = –5

(d) none of these

By solving (a), we get,

30 / 10 + 4 * 2 - 2 = 3 + 8 - 2 = 9 ≠ 15

By solving (b), we get,

5 * 2 + 4 / 2 * 2 = 10 + 2 * 2 = 10 + 4 = 14

By solving (c), we get, 

As we have an unknown symbol B, it can't be solved. 

Hence, the answer is (b).

Question 8:

Calculate 5A6M3P4Q8

= 5 + 6 - 3 * 4 / 8

= 5 + 6 - 3 * 0.5

= 5 + 6 - 1.5

= 11 - 1.5

= 9.5

Question 9:

Calculate (2A3M4P5)P(5M6P8Q4)

(a) –105 

(b) –120

(c) 120 

(d) none of these

= ( 2 + 3 - 4 * 5 ) * ( 5 - 6 * 8 / 4 )

= ( 5 - 20 ) * ( 5 - 6 * 2 )

= ( -15 ) * ( 5 - 12 )

= -15 * -7

= 105

Hence, the answer is (d).

Time to Think:

If ‘*’ indicates either ‘+’ or ‘*’, solve the following questions.

What is the maximum value of

1*2*3*4*5*6*7

(a) 5040 

(b) 5041

(c) 7!/2 

(d) none of these

What is the minimum value of

1*2*3*4

(a) 10 

(b) 9

(c) 11 

(d) 14