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**Directions (1 – 5): Study the following information carefully and answer the given questions:**

The given chart shows the number of students in three different schools in three different years.

**1) What is the difference between the total number of students from A in all the three years together and the number of boys from A in three years together?**

**Statement I:** The ratio of the number of boys to girls from A in 2015 is 3:2 and the number of girls from A in 2014 is 20 more than that of the number of boys from A in 2016.

**Statement II: **If the total number of students from A in 2014, 2015 and 2016 60%, 40% and 50% respectively are girls.

a) Only I

b) Only II

c) Either I or II sufficient

d) All I and II necessary to the answer the question

e) The question canâ€™t be answered even with all I and II

**2) What is the ratio of the boys to girls from C in 2014?**

**Which of the following statement is sufficient to answer the question?**

a) Ratio of the boys to girls from A and B in 2014 is 1: 3 and 2: 1 respectively and total students in 2014 from all the schools together 60% are girls.

b) The number of girls from C in 2014 is half of the number of boys from B in 2015.

c) Ratio of the number of boys to girls from C in all the years together is 3: 2 and the 50% of the students from C in 2015 is girls.

d) 40% of the students from C in 2014 is left and in this 80% of the students is girl.

e) Cannot be determine

**3) Number of girls from B in all the years together is what percent of the total number of students from B in all the years together?**

**Statement I: **Total number of students from B in 2017 is 280 and the ratio of the number of girls to boys from B in 2017 is 4: 3.

**Statement II: **60% of the total number of students from B in 2014 to 2017 is boys.

a) Only I

b) Only II

c) Either I or II sufficient

d) All I and II necessary to the answer the question

e) The question canâ€™t be answered even with all I and II

**4) Ratio of the boys to girls from A, B and C in 2016 is 7: 8, 4: 3 and 2: 3 respectively and the ratio of total number of boys from A, B and C in 2017 to the number of boys from A, B and C in 2016 is 1: 2. Total number of students from A, B and C in 2017 is 360.**

**From the statement given in the above question which of the following can be determined.**

**a) **Number of girls from A, B and C in 2017

**b) **Average number of boys from C in 2014 to 2017

**c) **Ratio of number of boys to girls from A, B and C in 2017

**d) **Difference between the number of girls and boys from all the three schools in all the years together (2014, 2015, 2016 and 2017)

a) Only A

b) Only A and D

c) Only A, C and D

d) Only A and C

e) All A, B, C and D

**5) 40% of the students from C in all the years together is girls and the number of boys from C in 2015 and 2016 is 180 and 80 respectively. What is the ratio of the number of girls from C in 2014, 2015 and 2016?**

a) 7: 12: 7

b) 2: 5: 2

c) 3: 11: 3

d) 6: 13: 6

e) None of these

**Direction (6 – 10): The following questions are accompanied by three statements I, II and III. You have to determine which statement/s is/are sufficient to answer the question. **

**6) What is the amount invested by Sam?**

**Statement I:** Total amount received by Rahul after 3 years is Rs.4800 at compound interest.

**Statement II: **Rahul and Sam invested their amount at the rate of 10% per annum.

**Statement III: **Rahul and Sam invested their amount at simple interest and compound interest respectively and the difference between the interests received by both after 2 years is Rs.1200.

a) Only I and II are sufficient

b) Only II and III are sufficient

c) Either II alone or I and II together to sufficient

d) All I, II and III necessary to the answer the question

e) The question canâ€™t be answered even with all I, II and III

**7) What is the sum of the ages of A and B?**

**Statement I:** Ratio of the ages of A to C is 4: 5 and the ratio of the ages of A to D is 1: 3.

**Statement II: **Sum of the ages of B, C and D is 125 years and 5 years ago the ratio of the ages of A to D is 3: 11.

**Statement III: **Dâ€™s age is 200% more than that of Aâ€™s age and the difference between the ages of A and D is 40 years.

a) Only I and II are sufficient

b) Only II and III are sufficient

c) Either II alone or I and II together to sufficient

d) All I, II and III necessary to the answer the question

e) The question canâ€™t be answered even with all I, II and III

**8) What is the total surface area of the cone?**

**Statement I:** Ratio of height of the cone to height of the cylinder is 2: 1.

**Statement II: **Height of the cylinder is equal to the perimeter of the square whose area is 9 cm^{2}.

**Statement III: **Radius of the cone is equal to length of the rectangle whose perimeter is 20 cm.

a) Only I and II are sufficient

b) Only II and III are sufficient

c) Either II alone or I and II together to sufficient

d) All I, II and III necessary to the answer the question

e) The question canâ€™t be answered even with all I, II and III

**9) There are four A, B, C and D partners in the business. What is the profit share of B?**

**Statement I:** A and B started the business with investment of Rs.x and Rs.2x respectively and after 6 months C and D joined them with investment of Rs.(x + 1000) and Rs.3x respectively.

**Statement II: **At the end of one years and profit Share of C is Rs.4000.

**Statement III: **At the end of one year the profit ratio of C and D is 2:3.

a) Only I and II are sufficient

b) Only II and III are sufficient

c) Either II alone or I and II together to sufficient

d) All I, II and III necessary to the answer the question

e) The question canâ€™t be answered even with all I, II and III

**10) What is the initial quantity of the milk in vessel A?**

**Statement I:** Ratio of the milk and water in vessel A and B is 3: 2 and 4: 3 respectively.

**Statement II: **28 liters of the mixture of B is poured into A and then the ratio of the milk and water in vessel A becomes 17: 12.

**Statement III: **10 liters of the mixture from vessel C is taken out and is poured into vessel A, then the ratio of the milk to water becomes vessel A is 5: 4.

a) Only I and II are sufficient

b) Only II and III are sufficient

c) Either II alone or I and II together to sufficient

d) All I, II and III necessary to the answer the question

e) The question canâ€™t be answered even with all I, II and III

**Answers :**

**Directions (1-5) :**

**1) Answer: b)**

**From statement I,**

Girls from A in 2015 = 2/5 * 250 =100

Boys from A in 2015 = 3/5 * 250 =150

So, Statement I alone is not sufficient to answer the question.

**From statement II,**

Girls from A in 2014 = 60/100 * 400 = 240

Boys from A in 2014 = 400 â€“ 240 = 160

Girls from A in 2015 = 40/100 * 250 = 100

Boys from A in 2015 = 250 â€“ 100 = 150

Girls from A in 2016 = 50/100 * 300 = 150

Boys from A in 2016 = 300 â€“ 150 = 150

Total number of students from A = 400 + 250 + 300 = 950

Boys from A = 150 + 150 + 160 = 460

Difference = 950 â€“ 460 = 490

So, Statement II alone is sufficient to answer the answer.

**2) Answer: a)**

**From option (A)**

Girls from A in 2014 = 400 * Â¾ =300

Girls from B in 2014 = 1/3 * 300 =100

Number of girls in 2014 = (400 + 300 + 200) * 60/100 = 540

Number of girls from C in 2014 = 540 â€“ 300 â€“ 100 = 140

Number of boys from C in 2014 = 200 â€“ 140 = 60

Required ratio = 60: 140 = 3: 7

This satisfied the given condition.

**From option (B)**

Number of boys from B in 2015 is not given

This not satisfied.

**From option (C)**

Number of girls from C in 2015 = 300 * 50/100 = 150

we cannot find the answer of the question.

This not satisfied.

**From option (D)**

Number of students left from C in 2014 = 200 * 40/100 = 80

Number of girls left from C in 2014 = 80 * 80/100 = 64

This not satisfied the given condition.

**3) Answer: d)**

**From statement I,**

Number of girls from B in 2017 = 4/7 * 280=160

Number of boys from B in 2017 = 3/7 * 280=120

So, statement I alone is not sufficient to answer the question.

**From statement II,**

60% of the total number of students from B in 2014 to 2017 is boys.

So, statement II alone is not sufficient to answer the question.

**From I and II,**

Total number of students from B in 2014 to 2017 = 300 + 100 + 350 + 280 = 1030

Number of boys from B in 2014 to 2017 = 1030 * 60/100 = 618

Number of boys from B in 2014 to 2016 = 618 â€“ 120 = 498

Number of girls from B in 2014 to 2016 = (300 + 100 + 350) â€“ 498 = 252

Required percentage = 252/750 * 100 = 33.6%

Both the statements are necessary to answer the question.

**4) Answer: d)**

Number of boys from A in 2016=7/15 * 300=140

Number of girls from A in 2016=8/15 * 300=160

Number of boys from B in 2016=4/7 * 350=200

Number of girls from B in 2016=3/7 * 350=150

Number of girls from C in 2016=3/5 * 150=90

Number of boys from C in 2016=2/5 * 150=60

Number of boys in 2016=140 + 200 + 60=400

Number of boys in 2017=1/2 * 400=200

Number of girls in 2017=360 â€“ 200=160

Required ratio boys to girls in 2017 = 200: 160=5:4

**5) Answer: a)**

Number of girls from C in 2015 = 300 â€“ 180 = 120

Number of girls from C in 2016 = 150 â€“ 80 = 70

Total number of girls from C = (200 + 300 + 150) * 40/100 = 260

Number of girls from C in 2014 = 260 â€“ 120 â€“ 70 = 70

Required ratio = 70: 120: 70

= 7: 12: 7

**Directions (6-10) :**

**6) Answer: e)**

**From statement I,**

Let the amount invests by Rahul = x

4800 = x * (1 + R/100)^{3}

So, Statement I alone is not sufficient to answer the question.

**From statement II,**

R = 10%

So, Statement II alone is not sufficient to answer the question.

**From statement III,Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **

Let the amount invests by Sam = x

Let amount invests by Rahul = y

SI = y * 2 * R/100 = yR/50

CI = x * (1 + R/100)^{2} â€“ x

CI â€“ SI = 1200

or

SI â€“ CI = 1200

So, Statement III alone is not sufficient to answer the question.

**7) Answer: a)**

**From statement I,**

A/C = 4/5

A/D = 1/3

So, Statement I alone is not sufficient to answer the question

**From Statement II,**

B + C + D = 125

(A â€“ 5)/(D â€“ 5) = 3/11

So, Statement II alone is not sufficient to answer the question

**From statement III,**

D = 300/100 * A

D: A = 3: 1

2x = 40

x = 20

A = 20 years

D = 3 * 20 = 60 years

So, Statement III alone is not sufficient to answer the question

**From statement I and II, **

A and Dâ€™s present age be x and 3x respectively

(A â€“ 5)/(D â€“ 5) = 3/11

(x – 5)/(3x – 5) = 3/11

= > 11x â€“ 55 = 9x â€“ 15

= > 2x = 40

= > x = 20

Present age of A and D is 20 and 60 years respectively

Câ€™s present age = 20/4 * 5 = 25 years

Bâ€™s present age = 125 â€“ (25 + 60) = 125 â€“ 85 = 40 years

Sum of the ages of A and B = (20 + 40) = 60 years

**Hence, statement I and II alone is sufficient to answer the given question.**

**9) Answer: e)**

**From statement I,**

Height of cone/height of the cylinder = 2/1

So, Statement II alone is not sufficient to answer the question

**From statement II,**

Area of the square = 9

Side of the square = 3

Perimeter of the square = 3 * 4 = 12 cm

Height of the cylinder = 12 cm

So, Statement II alone is not sufficient to answer the question

**From statement III,**

Radius of the cone = length of the rectangle

Perimeter of the rectangle = 2 * (l + b) = 20

So, Statement III alone is not sufficient to answer the question

**10) Answer: d)**

**From statement I,**

A = x

B = 2x

C = (x + 1000)

D = 3x

So, Statement I alone is not sufficient to answer the question

**From Statement II,**

Câ€™s share = Rs.4000

So, Statement I alone is not sufficient to answer the question

**From statement III,**

Profit ratio of C/D = 2/3

So, Statement III alone is not sufficient to answer the question

**From I, II and III**

Profit ratio of A, B, C and D = x * 12: 2x * 12: (x + 1000) * 6: 3x * 6

=12x: 24x: (6x + 6000): 18x

(6x + 6000)/18x = 2/3

6x + 6000 = 12x

x = 1000

Profit ratio = 12000: 24000: 12000: 18000

= 2: 4: 2: 3

Bâ€™s profit share = 4/2 * 4000 = 8000

All the statements are necessary to answer the question.

**10) Answer: a)**

**From statement I,**

Milk and water in A = 3: 2

Milk and water in B = 4: 3

So, Statement I alone is not sufficient to answer the question

**From statement II,**

Vessel B mixture = 28

Ratio of the milk and water in A = 17: 12

So, Statement II alone is not sufficient to answer the question

From statement III,

Mixture of C = 10

Ratio of milk and water in C = 5: 4

So, Statement III alone is not sufficient to answer the question

**From I and II**

Milk in 28 liters of B = 4/7 * 28 = 16 liters

Water in 28 liters of B = 3/7 * 28 = 12 liters

3x + 16/2x + 12 = 17/12

34x + 204 = 36x + 192

2x = 12

x = 6

Milk in vessel A = 3 * 6 = 18 liters

So, Statement I and II are necessary to answer the question.