Aptitude ➤ Simplifications

#### Simplifications : Important Facts and Formulae

I. ‘BODMAS’ Rule : This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of a given expression.

Here, ‘B’ stands for 'bracket' ,
'O'for ‘of’ ,
‘D’ for 'division'
‘M’ for ‘multiplication’,
‘S’ for ‘subtraction’.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (), {} and [].
After removing the brackets, we must use the following operations strictly in the order:
(1) of (2) division (3) multiplication (4)addition (5)subtraction.

II. Modulus of a real number : Modulus of a real number a is defined as
|a| = { a, if a > 0;
|a| = { -a, if a < 0;
Thus, |5| = 5 and |-5| = -(-5) = 5.

III. Virnaculum (or bar): When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.
Question 1
Q1.  Simplify : b - [b - (a + b) - { b - (b - a - b )} + 2a] .
Question 2
Q2.  What value will replace the question mark in the following equation ?
(9/2) + (19/6) + ? + (7/3) = (67/5).
Question 3
Q3.  If 2x + 3y + z = 55, x + z - y = 4 and y - x + z = 12, then what are the values of x , y and z respectively?
Question 4
Q4.  A board 7 ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Question 5
Q5.  A man divides Rs. 8600 among 5 sons, 4 daughters and 2 nephews . If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews , how much does each daughter receive ?  