## Aptitude :: SimplificationPage 1

1.'BODMAS' Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
Here B - Bracket,
O - of,
D - Division,
M - Multiplication,
S - 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:
(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

2. Modulus of a Real Number:
Modulus of a real number a is defined as
|a| = a, if a > 0
-a, if a < 0
Thus, |5| = 5 and |-5| = -(-5) = 5.

3. Virnaculum (or Bar):
When an expression contains Virnaculum, before applying the 'BODMAS' rule, we simplify the expression under the Virnaculum.

1.

 Simplify: 5005 - 5000 ÷ 10 (a)4505 (b)4605 (c)4705 (d)4805
Answer is: ALet, 5005 â€“ 5000/10 = 5005 â€“ 500 = 4505

2.

 Simplify: 343 ÷ 49 ÷ 7 ÷ 7 (a)1/12 (b)1/13 (c)1/7 (d)1/9
Answer is: CLet , 343 x 1/49 x 1/7 x 1/7 = 1/7

3.

 The value of 1001 ÷ 11 of 13 is : (a)8 (b)5 (c)6 (d)7
Answer is: D⇒ 1001 ÷ 11 x 13
⇒ 1001/(11 x 13) = 7.

4.

 The value of 25 â€“ 5 [2 + 3 {2 â€“ 2 (5 â€“ 3) + 5} â€“ 10] ÷ 4 is: (a)22.25 (b)23.75 (c)23.25 (d)22.75
Answer is: B⇒ 25 â€“ 5 [2 + 3 {2 â€“ 2 (5 â€“ 3) + 5} â€“ 10] ÷ 4
⇒ 25 â€“ 5 [2 + 3 {2 â€“ 2 x 2 + 5} â€“ 10] ÷ 4
⇒ 25 â€“ 5 [2 + 3 {2 â€“ 4 + 5} â€“ 10] ÷ 4
⇒ 25 â€“ 5 [2 + 3 {3} â€“ 10] ÷ 4 = 25 â€“ 5 [2 + 9 â€“ 10] ÷ 4
⇒ 25 â€“ 5 ÷ 4
⇒ 25 â€“ 1.25 = 23.75

5.

 What mathematical operation should come at the place of â€˜?â€™ in the equation: 2 ? 6 â€“ 12 ÷ 4 + 2 = 11 (a)+ (b)- (c)/ (d)x
Answer is: D ⇒ 2 ? 6 â€“ 12 ÷ 4 + 2 = 11
⇒ 2 X 6 â€“ 12 ÷ 4 + 2 = 11
⇒ 2 X 6 â€“ 3 + 2 = 11 = 2 X 6 = 11 +3 -2
⇒ 2 X 6 = 12
So, in place of X, we apply x(multiply)

6.

 The value of [(6 + 6 + 6 + 6) Ã· 6]/(4 + 4 + 4 + 4 Ã· 4) is equal to ? (a)13/4 (b)4/13 (c)9/4 (d)4/9
Answer is: Bâ‡’ (24 Ã· 6)/(4 + 4 + 4 + 1) = 4/13

7.

 Evaluate: [8 - {5 - ( - 3 + 2)} Ã· 2]/[(5 - 3) - (6 - 3) Ã·3] (a)3 (b)4 (c)5 (d)6
Answer is: Câ‡’ [8 - {5 - ( - 3 + 2)} Ã· 2]/[(5 - 3) - (6 - 3) Ã·3] = [8 - {5 - (-1)} Ã·2]/[2 - 3 Ã·3]
â‡’ (8 - 6 Ã· 2)/( 2 - 1) = 8 â€“ 3 = 5

8.

 If 1/3 + 1/2 + 1/X = 4, then X = ? (a)6 / 19 (b)19 / 6 (c)5 / 19 (d)19 / 5
Answer is: A1/3 + 1/2 + 1/X = 4
â‡’ 1/X = 4 - 1/3 - 1/2
â‡’ 1/X = (24 - 2 - 3)/6 = 19/6
â‡’ X = 6/19