**1).**In a class of 24 students, each student shakes hand with everyone els. In another class of 32 students, each student shakes hand with all other students. What is the difference between total number of hand shakes in the 2 classes?

a) 180

b) 200

c) 22

d) 240

e) 260

**2).**Which of the following series of discounts is the best for a customer?

(A) Successive discounts of 10% ,20%,30%

(B) Successive discounts of 20%,20%,20%

(C) Successive discounts of 15%,15%,15%,15%

(D) Successive discounts of 20%,40%

a) A

b) B

c) C

d) D

e) A and B

**3).**A,B and C can do piece of work in 11 days,20 days and 55 days respectively, working alone. How soon can the work be done if a is assisted by B and C on alternate days/

a) 6

b) 7

c) 8

d) 9

e) 10

**4).**A,B are start walking around a Circular park of radius 70m. They start at the same point, and A goes clockwise at 10m/s, while b goes anti-clockwise at 20m/s.How many times will they cross each other at the starting point if they walk for 30 minutes?

a) 20

b) 40

c) 60

d) 80

e) None of the above

**5).**Ram is 3 times as old as his brother. Ram’s father is 3 times older than Ram. In 9 years , Ram will be 1.5 times the age of his brother. What will be the age of Ram’s father when Ram is 1.5 times the age of his brother?

a) 27

b) 36

c) 45

d) 54

e) 63

**Directions (6-10):Each of the questions below consists of a question and two statements numbered I and II given below it.You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements.**

**6).**Is it more profitable for Company M to produce Q?

**I.**Product R sells at a price four times that of Q

**II.**One unit of Q requires 2 units of labour, while one unit of R requires 5 units of labour. There is a no other constraint on production.

If the question can be answered with the help of statement I alone,

If the question can be answered with the help of statement II alone,

If both,statement I and statement II are needed to answer the question

If the question cannot be answered even with the help of both the statements.

If the data in either statement I or statement II alone is sufficient to answer the question

**7).**A man distributed 43 chocolates to his children. How many of his children are more than five years old?

**I.**A child older than five years gets 5 chocolates

**II.**A child 5 years or younger in age gets 6 chocolates.

If the question can be answered with the help of statement I alone,

If the question can be answered with the help of statement II alone,

If both,statement I and statement II are needed to answer the question

If the question cannot be answered even with the help of both the statements.

If the data in either statement I or statement II alone is sufficient to answer the question

**8).**What is the radius of the circle/

**I.**Ratio of its area to circumference is>7.

**II.**Diameter of the circle is ≤ 32.

If the question can be answered with the help of statement I alone,

If the question can be answered with the help of statement II alone,

If both,statement I and statement II are needed to answer the question

If the question cannot be answered even with the help of both the statements.

If the data in either statement I or statement II alone is sufficient to answer the question.

**9).**X says to Y,”I am 3 times as old as you were 3 years ago”.How old is X?

**I.**Y ‘s age 17 years from now is same as X’s present age.

**II.**X’s age nine years from now is 3 times Y’s present age.

If the question can be answered with the help of statement I alone,

If the question can be answered with the help of statement II alone,

If both,statement I and statement II are needed to answer the question

If the question cannot be answered even with the help of both the statements.

If the data in either statement I or statement II alone is sufficient to answer the question

**10).**What is the value of prime number x?

**I.**X

^{2}+ x is a two digit number greater than 50

**II.**X

^{3}is a three digit number.

If the question can be answered with the help of statement I alone,

If the question can be answered with the help of statement II alone,

If both,statement I and statement II are needed to answer the question

If the question cannot be answered even with the help of both the statements.

If the data in either statement I or statement II alone is sufficient to answer the question

**Answers:**

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

**Solution:**

**1).**1 st class : Total Hand shakes = 24 × 23 /2 = 12 × 23 =276

2

^{nd}class :Total Hand shakes =32 × 31 / 2 = 16 × 31 = 496Difference =220

**Answer : c**

**2).**consider the price as 100

A = 100 × 0.9 × 0.8 × 0.7 =50.4

B = 100 × 0.8 × 0.8 × 0.8=51.2

C = 100 × 0.85 × 0.85 × 0.85 ×0.85 ~ =52.2

D = 100 × 0.8 × 0.6 =48

We see that the maximum discount of 52% (100-48) is on D, which is the best for a customer.

**Answer : d**

**3).**Work done by A and B in one day = 1/11 + 1/20 =31/220

Work done by A and C in one day = 1/11 + 1/55 =6/55

Work done in 2 days = 31 /220+6/55=55/220 = ¼

Hence, 1/4 of the work is done in 2 days

Hence, it takes 8 days to finish the work

**Answer : c**

**4).**Radius = 70m, So circumference = 2 × (22/7) × 70 =440m

Relative speed = 10 +20 = 30m/s

They will meet everytime at the starting point when the distance covered by both put together is a multiple of 440

LCM of (440,30) = 44 × 30

So, they will meet at starting point every 44 seconds.

In 30minutes, they will meet =1800/44 =40.9

So they will meet 40 times (we need to ignore the decimal part).

**Answer : b**

**5).**Let the age of Ram be R, brother be B

R=3B

And (R + 9 ) =1.5(B + 9)

3B + 9 =1.5B + 13.5

1.5B =4.5 or B = 3 years R= 9 years.

Father current age = 4R(Since father is 3 times older than Ram, his age is R + 3 R, and not 3R)

Father age when Ram is 1.5 times the age of his brother = 4R + 9 = 45.

**Answer : c**

**6).**from statement I :

Let the price of product Q be ‘P’

Then the price of product R is 4P

From Statement II:

Cost of product Q =2

Cost of product R=5

Therefore,

Profit percentage of product Q = (P-2 ) × 100/2 =50(P-2)=50P – 100

Profit percentage of product R = (4P -5) × 100/5=20(4P-5)=80P-100

Hence, product R is more profitable.

Both statements are required to answer the question

**Answer :c**

**7).**From both statement I and II:

Let the number of chocolates received by child older than 5 years be x and that of for child than 5 years or younger be y

Therefore,

5x + 6 y = 43

Since x and y has to be natural numbers, the solution for the above equation will be x=5 and y=3

Hence, 5 children are older than 5 years

**Answer : c**

**8).**Let the radius of the circle be r units

From statement 1:

[πr^2]/ [ 2 πr ]> 7 or r> 14

From statement II:

2r≤32

R ≤ 16

Hence, r can be 15 or 16 units

Hence,

**Answer : d**

**9).**Let the current ages of X and Y be a and b respectively

From the question:

A=3(a-b)

From statement I:

A=b + 17

B = a-17

Therefore, a = 3(a-17-3)

a=3a-60

2a=60

A=30

Hence, X is 30 years old

From statement II:

a + 9 = 3b

b=(a+9)/3

Substituting this in first equation,

A=a+9-9

Hence, no result

Therefore, statement I alone is sufficient

**Answer :a**

**10).**From statement I :

(x

^{2}+x) should be less than 100 and greater than 50This is possible only for 3 numbers i.e.7,8,9

7

^{2}+ 7 =568

^{2}+ 8 = 729

^{2}+ 9 = 90But only 7 is prime number. Hence,x=7

From statement II:

The value of x can 5 or 7, since both 5

^{3}and 7^{3}is a three digit numberHence, only statement I alone is sufficient to answer the question

**Answer : a**