SBI Clerk Mains Quantitative Aptitude (Day-54)

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Date Sufficiency

Direction (1-5): 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.

1) 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 can’t be answered even with all I, II and III

2) 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: D’s age is 200% more than that of A’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 can’t be answered even with all I, II and III

3) 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 cm2.

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 can’t be answered even with all I, II and III

4) 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 can’t be answered even with all I, II and III

5) 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 can’t be answered even with all I, II and III

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:

1) 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,                   

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 – x

CI – SI=1200

or

SI – CI=1200

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

2) 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 – 5)/(D – 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 D’s present age be x and 3x respectively

(A – 5)/(D – 5) = 3/11

(x – 5)/(3x – 5) = 3/11

= > 11x – 55 = 9x – 15

= > 2x = 40

= > x = 20

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

C’s present age = 20/4 * 5 = 25 years

B’s present age = 125 – (25 + 60) = 125 – 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. 

3) 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

4) 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,

C’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

B’s profit share=4/2 * 4000=8000

All the statements are necessary to answer the question.

5) 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.

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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