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**Data sufficiency**

**Direction (1 – 5): The following questions are accompanied by three statements I and II. You have to determine which statement is/are sufficient to answer the question. **

**1) Written in digit form, 24x82y. If the digit is divisible by 9, what is the value of x and y?**

**Statement I:** Difference between x and y is 1.

**Statement II: **x * y = 30

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 can’t be answered even with all I and II

**2) What is the volume of the cylinder?**

**Statement I:** Surface area of the sphere is equal to the curved surface area of the cone and the radius of the cylinder is equal to the radius of the sphere.

**Statement II: **Radius of the sphere is equal to the radius of the cylinder and the radius and height of the cone is 7 cm and 24 cm respectively.

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 can’t be answered even with all I and II

**3) Find the value of x?**

**Statement I:** If A’s age is x% of more than that of B’s age and D’s age is 30% more than C.

**Statement II: **B’s age is 20% more than C and A’s age is 50% more than D.

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 can’t be answered even with all I and II

**4) A, B and C started the business. What is C’s profit share?**

**Statement I:** A and B invests Rs.6000 and Rs.8000 respectively and after 6 months C joined with them with the investment of Rs.6000.

**Statement II: **Total profit is Rs.28000 and the B’s investment period is 8 months.

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 can’t be answered even with all I and II

**5) A bag contains x red balls and y blue balls. Find the value of x?**

**Statement I:** The probability of two red balls selected randomly is 1/6.

**Statement II: **The probability of two blue balls is selected at randomly is 5/18.

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 can’t be answered even with all I and II

**Data Interpretation**

**Direction (6 – 10): Study the following information carefully and answer the given questions?**

The given line graph shows the number of employees in three different department from five different companies – A, B, C, D and E in 2015.

**6) If the number of employees in IT department in each company increased by 40% and the number of employees in Sales department in each company decreased by 20% from 2015 to 2016. Ratio of the number of male to female employees in IT department and sales department in 2016 is 3: 2 and 5: 3 respectively. What is the difference between the number of female employees in IT and sales department together and the number of male employees in IT and sales department together?**

a) 384

b) 376

c) 398

d) 372

e) 386

**7) What is the difference between the total number of employees in HR department from all the companies together and the total number of employees in sales department from all the companies together?**

a) 100

b) 150

c) 200

d) 250

e) None of these

**8) If the number of employees from C, D and E in HR department increased by 10%, 20% and 20% respectively from 2015 to 2016. If the ratio of the male to female employees in HR department from C, D and E in 2016 is 2: 3, 1: 2 and 2: 3 respectively, then what is the number of male employees in HR department from C, D and E in 2016 together is approximately what percent of the number of female employees in HR department from C, D and E in 2016 together?**

a) 60%

b) 62%

c) 64%

d) 66%

e) 69%

**9) In A, C and E ratio of the male to female employees in IT department is 7: 8, 3: 2 and 2: 1 respectively. What is the ratio of the total number of female employees in IT department from A, C and E together to the total number of male employees in IT department from A, C and E together?**

a) 11:16

b) 12:19

c) 17:23

d) 3:4

e) None of these

**10) What is the ratio of the total number of employees from B in all the departments together to the total number of employees from D in all the departments together?**

a) 7: 5

b) 11: 9

c) 13: 11

d) 16: 13

e) None of these

**Answers:**

**Directions (1-5):**

**1) Answer: E**

**From statement I,**

Sum of the digits = 2 + 4 + x + 8 + 2 + y = 16 + x + y

The number is divisible by 9, so sum of the digits is divisible by 9.

So, x + y = 2 or 11

x – y = 1 or y – x = 1

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

**From statement II,**

Sum of the digits = 2 + 4 + x + 8 + 2 + y = 16 + x + y

The number is divisible by 9, so sum of the digits is divisible by 9.

So, x + y = 2 or 11

x * y = 30

So, x + y = 2 is not possible.

x + y = 11

x = 11 – x

x * (11 – x) = 30

11x – x^{2 }= 30

x^{2}– 11x + 30 = 0

(x – 5) (x – 6) = 0

x = 5, 6

If x = 5 means y = 6 and if x = 6 means y = 5

So the number forms, 24x82y = 245826 or 246825

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

**2) Answer: E**

**From statement I,**

Surface area of the sphere = 4πr^{2} = 4 * 22/7 * r^{2}

CSA of cone = πrl = 22/7 * r * l

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

From statement I,

Radius of the cone = 7 cm

Height of the cone = 24 cm

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

**3) Answer: D**

**From statement I,**

A = [(100 + x)/100] * B

D = 130/100 * C

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

**From statement II,**

B = 120/100 * C

A = 150/100 * D

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

**From I and II,**

A = [(100 + x)/100] * B

D = 130/100 * C

B = 120/100 * C

A = 150/100 * D

2A/3 = D

2A/3 = 13/10 * C

20A/39 = C

B = 6/5 * 20A/39

B = 8A/13

A = (100 + x)/100 * 8A/13

1300 = 800 + 8x

500 = 8x

x = 62.5

**Both the statements are necessary to answer the question.**

**4) Answer: E**

**From statement I,**

A’s investment = Rs.6000

B’s investment = Rs.8000

C’s investment = Rs.6000

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

**From statement II,**

Total profit = Rs.28000

B’s investment period = 8 months

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

**From I and II,**

A and C’s investment period is not given.

Both the statements are not necessary to answer the question.

**5) Answer: E**

**From statement I,**

1/6 = x * (X – 1)/(x + y) * (x + y – 1)

1/6 = (x^{2} – x)/(x^{2} + xy – x + xy + y^{2} –y)

6(x^{2} – x) = x^{2} + xy – x + xy + y^{2} –y

6x^{2} – 6x = x^{2} + xy – x + xy + y^{2} –y

5x^{2} – 2xy – 5x – y^{2} +y = 0

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

**From statement II,**

5/18 = y * (y – 1)/(x + y) * (x + y – 1)

18(y^{2} – y) = 5(x^{2} + xy – x + xy + y^{2} –y)

18y^{2} – 18y = 5x^{2} + 10xy – 5x + 5y^{2} –5y

13y^{2} – 13y – 5x^{2} – 10xy + 5x = 0

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

**Directions (6-10):**

**6) Answer: A**

Number of employees in IT department from A in 2016 = 150 * 140/100 = 210

Number of employees in IT department from B in 2016 = 200 * 140/100 = 280

Number of employees in IT department from C in 2016 = 100 * 140/100 = 140

Number of employees in IT department from D in 2016 = 200 * 140/100 = 280

Number of employees in IT department from E in 2016 = 150 * 140/100 = 210

Total number of employees in IT department in 2016

= 210 + 280 + 140 + 280 + 210 = 1120

Male employees in IT department in 2016 = 3/5 * 1120 = 672

Female employees in IT department in 2016 = 2/5 * 1120 = 448

Number of employees in Sales department from A in 2016 = 100 * 80/100 = 80

Number of employees in Sales department from B in 2016

= 250 * 80/100 = 200

Number of employees in Sales department from C in 2016

= 150 * 80/100 = 120

Number of employees in Sales department from D in 2016 = 100 * 80/100 = 80

Number of employees in Sales department from E in 2016

= 200 * 80/100 = 160

Total number of employees in sales department in 2016

= 80 + 200 + 120 + 80 + 160 = 640

Male employees in sales department in 2016 = 5/8 * 640 = 400

Female employees in sales department in 2016 = 3/8 * 640 = 240

Male employees in sales and IT department = 400 + 672 = 1072

Female employees in sales and IT department = 240 + 448 = 688

Difference = 1072 – 688 = 384

**7) Answer: B**

Total number of employees in HR department

= 200 + 100 + 250 + 150 + 250 = 950

Total number of employees in sales department

= 100 + 250 + 150 + 100 + 200 = 800

Difference = 950 – 800 = 150

**8) Answer: B**

Number of employees in HR department from C in 2016

= 250 * 110/100 = 275

Number of male employee in HR department from C in 2016

= 2/5 * 275 = 110

Number of female employees in HR department from C in 2016

= 275 * 3/5 = 165

Number of employees in HR department from D in 2016

= 150 * 120/100 = 180

Number of male employee in HR department from D in 2016

= 1/3 * 180 = 60

Number of female employees in HR department from D in 2016

= 2/3 * 180 = 120

Number of employees in HR department from E in 2016

= 250 * 120/100 = 300

Number of male employee in HR department from E in 2016

= 2/5 * 300 = 120

Number of female employees in HR department from E in 2016

= 3/5 * 300 = 180

Required percentage

= (110 + 60 + 120)/(165 + 120 + 180) * 100 = 62%

**9) Answer: C**

Number of male employee in IT department from A in 2015 = 150 * 7/15 = 70

Number of female employees in IT department from A in 2015

= 150 * 8/15 = 80

Number of male employee in IT department from C in 2015 = 3/5 * 100 = 60

Number of female employees in IT department from C in 2015 = 2/5 * 100 = 40

Number of male employee in IT department from E in 2015 = 2/3 * 150 = 100

Number of female employees in IT department from E in 2015 = 1/3 * 150 = 50

Required ratio = (80 + 40 + 50): (70 + 60 + 100)

=170: 230

=17: 23

**10) Answer: B**

Required ratio = (200 + 100 + 250): (200 + 150 + 100)

= 550: 450

= 11: 9

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