**Simplification**

**Simplification-aptitude-questions-answers-basics**

**Simplification
Aptitude basics, practice questions, answers and explanations **

**Prepare for companies tests and interviews**

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', 'A' for 'Addition'
and '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:

(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

Eg: (-5)(4)(2)(-1/2)(3/4)=?

-5*4*2*-1/2*3/4= 15

II. **Modulus of a Real Number:**
Modulus of a real number a is defined as

a|= a, if a>0 or

|a|= -a, if a<0

Thus, |5|= 5 and |-5|= -(-5)=5

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

**Exercise Questions**

1.((469 + 174)^{2} - (469 - 174)^{2})/(469
x 174) = ?

a. 2

b. 4

c. 295

d. 643

Answer: Option b

Explanation: Given exp. = ((a + b)^{2}
- (a - b)^{2})/ab

=4ab/ab =
4

2. David gets on the elevator at the
11th floor of a building and rides up at the rate of 57 floors per minute. At
the same time, Albert gets on an elevator at the 51st floor of the same building
and rides down at the rate of 63 floors per minute. If they continue travelling
at these rates, then at which floor will their paths cross ?

a. 19

b. 28

c. 30

d. 37

Answer: Option c

Explanation: Suppose their paths cross
after x minutes. Then, 11 + 57x = 51 - 63x => 120x = 40

x=1/3

Number of floors covered by David in
(1/3) min. = (1/3)*57= 19

So, their paths cross at (11 +19) i.e.,
30th floor.

3. A man has some hens and cows. If the
number of heads be 48 and the number of feet equals 140, then the number of
hens will be:

a. 22

b. 23

c. 24

d. 26

Answer: Option d

Explanation: Let the number of hens be x and the number of cows be y.

Then, x + y = 48 .... (i)

and 2x + 4y = 140 => x +
2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y =
22.

Therefore, The required answer = 26.

4. In a regular week, there are 5
working days and for each day, the working hours are 8. A man gets Rs. 2.40 per
hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432
in 4 weeks, then how many hours does he work for ?

a. 160

b. 175

c. 180

d. 195

Answer: Option B

Explanation: Suppose the man works
overtime for x hours.

Now, working hours in 4 weeks = (5 * 8 *
4) = 160.

Therefore, 160 * 2.40 + x * 3.20 = 432

=> 3.20x = 432 - 384 = 48

=> x = 15.

Hence, total hours of work = (160 + 15)
= 175.

5. One-third of Rahul's savings in
National Savings Certificate is equal to one-half of his savings in Public
Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved
in Public Provident Fund ?

a. Rs. 30,000

b. Rs. 50,000

c. Rs. 60,000

d. Rs. 90,000

Answer: Option C

Explanation: Let savings in N.S.C and
P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,

(1/3)x= (1/2)(150000-x)

x/3+x/2=75000

5x/6=75000

x=75000*6/5= 90000

Therefore, Savings in Public Provident
Fund = Rs. (150000 - 90000) = Rs. 60000

6. A sum of Rs. 1360 has been divided
among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C
gets. B's share is:

a. Rs.120

b. Rs. 160

c. Rs.240

d. Rs.300

Answer: Option C

Explanation: Let C's share = Rs. x

Then, B's share = Rs. x/4; A's share =
Rs.2/3 * x/4= Rs. x/6

Therefore x/6 + x/4 + x = 1360

17x/12 = 1360

x= 1360*12/17= Rs.960

Hence, B's share= Rs.960/4= Rs.240

7. If a-b= 3 and a2+b2=29, find the
value of ab

a. 10

b. 12

c. 15

d. 18

Answer: Option A

Explanation: 2ab = (a2 + b2) - (a - b)2

= 29 - 9 = 20

=> ab = 10.

8. If 45-[28-{37-(15-*)}]= 58, then * is
equal to:

a. -29

b. -19

c. 19

d. 29

Answer: Option c

Explanation: 45-[28-{37-(15-*)}]= 58
=> 45-[28-{37-15+*}]=58

45-[28-37+15-*]=58 =>
45[43-37-*]=58

45-[6-*]=58 => 45-6+*=58

39+*=58 => *=58-39

= 19