**Directions (Q. 1-5):**Each of these questions consists of a questions followed by information in three statements.

You
have to study the question and the statements and decide that information in
which of the statement(s) is/are necessary to answer the question.

**1).**What is the capacity of the cylindrical tank?

I. Radius of the base is half of its height.

II. Area of the base is 616 square
meters.

III. Height of the cylinder is 28
meters.

a)
Only I and II

b)
Only II and III

c)
Only I and III

d)
All I, II and III

e)
Any two of the three

**2).**What is the speed of the train?

I. The train crosses a signal pole in 18
seconds

II. The train crosses a platform
of equal length in 36 seconds.

III. Length of the train is 300
meters.

a)
I and III only

b)
II and III only

c)
I and II only

d)
III and either I or II only

e)
Any two of three

**3).**What is the staff strength of company X?

I. Male and female employees are in the ratio
2:3 respectively.

II. Of the officer employees 80%
are male.

III. Total number of officer is
132.

a)
I and III only

b)
II and either III or I only

c)
All I, II and III

d)
Any two of three

e)
Cannot be determined

**4).**What is the two digit number?

I. Number obtained by interchanging the digits
is more than the original number by 9.

II. Sum of the digits is 7.

III. Difference between the digits
is 1.

a)
I and III only

b)
I and II only

c)
II and III only

d)
All I, II and III

e)
Cannot be determined

**5).**How many articles were sold?

I. Total profit earned was Rs. 1,596/-

II. Cost – price per article was
Rs. 632/-

III. Selling price per articles
was Rs. 765/-

a)
II and III only

b)
I and II only

c)
All I, II and III

d)
Any two of the three

e)
Question cannot be answered even
with the information in all three statements

**6).**Simplify: ( √2 + √4 - √6)

^{-1}

a)
( 1 + √2 + √3) / 4

b)
(1 - √2 + √3) / 4

c)
(1 + √2 - √3) / 4

d)
(1 - √2 - √3) / 8

e)
None of these

**7).**(15 + 8 – 15 ÷ (40 × 1 ÷ 8)) × 12 ÷ (8 – 4) + (6 ÷ 2 + 7 ×2 – 9)×1 ÷2

a)
48

b)
56

c)
121

d)
64

e)
None of these

**8).**(12 × 8 – 9 ÷ (45 × 1 ÷ 405)) × 6 ÷ (19 – 14) + (1 ÷ 2 + 7× 2.5 – 9 + 1.5) × 2

a)
17

b)
25

c)
31

d)
39

e)
None of these

**9).**(14 + 72 ÷ 4 × (300 × 1 ÷ 270)) × 6 ÷( 14 – 11) + ( 1 ÷ 2 + 12 × 3.5 – 9) × 4

a)
108

b)
128

c)
134

d)
187

e)
202

**10).**Evaluate: (0.943 × 0.943 – 0.943 × 0.057 + 0.057 × 0.057) / (0.943 × 0.943 × 0.943 + 0.057 × 0.057 × 0.057)

a)
0.886

b)
1. 1286

c)
0.32

d)
0.781

e)
None of these

**Answers:**

**1)e 2)d 3)e 4)b 5)c 6)a 7)d 8)d 9)e 10)e**

__Solution:__**1).**The capacity of the cylindrical tank is nothing but its volume

Volume
of the tank = V = pr

^{2}h
Consider
statement I and II:

Area
of the base = 616 sq.m

pr

^{2}= 616
Hence,
radius value can be calculated

From
statement I, we can calculate the height of the cylinder

Hence,
from statement I and II, volume of the tank can be calculated

Consider
statement I and III:

Height
of the cylinder is given and from statement I, radius of the cylinder can be
calculated

Hence,
from statements I and III, volume of the tank can be calculated

Consider
statements II and III:

Radius
of the cylinder can be calculated from statement II and height is given in
statement III.

Hence,
from these statements also, volume of the tank can be calculated

Hence,
any two of the three statements is sufficient to find the capacity of the
cylinder

**Answer: e)**

**2).**Consider statement I and III:

Length
of the train = 300 m

Speed
of the train = 300/18 = 16.67 m/s

Consider
statement II and III:

Length
of train = length of platform = 300 m

Speed
= 600/36 = 16.67 m/s

Consider
statement I and II:

Since
the length of the train is not known, we cannot determine the speed of the
train

Hence,
statement III is necessary and then either statement I or II is sufficient to
determine the speed of the train

**Answer: d)**

**3).**From the statements II and III:

Number
of male officer employees = 0.8 ×132 = 105 and female officer employees = 27

But
there is no information about non-officer employees number or ratio
corresponding to officer employees. Hence, using all the statements also, we
cannot determine the staff strength

**Answer: e)**

**4).**Let the number be (10x +y)

From
statement I:

(10y
+x) – (10x + y) = 9

9y
– 9x = 9

Y
–x = 1

From
statement II:

X
+ Y = 7

Hence,
solving both, x =3 and y = 4

Hence,
the two digit number is 34

**Answer: b)**

**5).**Let the number of articles sold be N

Combining
all the statements,

765N
– 632N = 1596

133N
= 1596

N
= 12

**Answer: c)**

**6).**( √2 + √4 - √6)

^{-1}=

^{ }( √2 + √4 + √6) / [(√2 + √4)

^{2}– (√6)

^{2}]

=
(√2 + √4 + √6) / (2 + 4 + 2√8 - 6) à (√2 + √4 + √6) / 2√8

=
(√2 + √4 + √6) / 4√2 à (2 + √8 + √12) / 8

=
2(1√2 + √3) / 8 à
(1 + √2 + √3) / 4

**Answer: a)**

**7).**40×1÷8 = 40/8 = 5

15
÷ (40×1÷8) = 15/5 = 3

(15
+ 8 – 15 ÷ (40×1÷8)) = 15 + 8 – 3 = 20

12÷(8-4)
= 12/4 = 3

(15
+ 8 – 15 ÷(40×1÷8)) × 12÷(8-4) = 20×3 = 60

(6
÷ 2 + 7 × 2 - 9)× 1÷2 = (3 + 14 – 9) / 2 = 4

(15
+ 8 – 15 ÷(40×1÷8)) × 12÷(8-4) + (6 ÷ 2 + 7 × 2 - 9)× 1÷2 = 60 + 4 = 64

**Answer: d)**

**8).**12×8 = 96

9÷(45
×1÷ 405) = 9 ÷ (1/9) = 9×9 = 81

(12
× 8 – 9 ÷(45×1÷405)) = 96 – 81 = 15

(12
× 8 – 9 ÷(45×1÷405)) × 6 ÷ (19-14) = 15 × 6 / 5 = 18

(1
÷ 2 + 7 × 2.5 – 9 + 1.5) = 0.5 + 17.5 -7.5= 10.5

(1
÷ 2 + 7 × 2.5 – 9 + 1.5) × 2 = 21

(12
× 8 – 9 ÷(45×1÷405)) × 6 ÷ (19-14) + (1 ÷ 2 + 7 × 2.5 – 9 + 1.5) × 2 = 18+21 =
39

**Answer: d)**

**9).**300 × 1 ÷ 270 = 10/9

72
÷ 4 = 18

72
÷ 4 × (300 × 1 ÷ 270) = 18 × 10/9 = 20

(14
+ 72 ÷ 4 × (300 × 1 ÷ 270)) = 14 + 20 = 34

6
÷ (14 - 11) = 6/3 = 2

(1÷2
+ 12 × 3.5 - 9)× 4 = (0.5 + 42 - 9)×4 = 134

(14
+ 72 ÷ 4 × (300 × 1 ÷ 270)) × 6 ÷ (14 - 11) + (1÷2 + 12 × 3.5 - 9)× 4

=
34 × 2 + 134 = 68 + 134 = 202

**Answer: e)**

**10).**Let a = 0.943 and b = 0.057

Therefore,
the given expression will be = (a

^{2}– ab + b^{2}) / (a^{3}+ b^{3}) = 1/(a+b)
So,
the expression = 1/ (0.943 + 0.057) = 1

**Answer: e)**

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