SBI Clerk Mains Quantitative Aptitude (Day-10)

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Quadratic equation

Directions (1 – 5): In the following questions, two equations I and II are given. You have to solve both equations and give answer as,

a) If x > y

b) If x ≥ y

c) If x < y

d) If x ≤ y

e) If x = y or the relation cannot be established.

1) I) x2 – 40x + 391 = 0

II) y2 – 8y – 345 = 0

 

2) I) 2x2 + 28x + 98 = 0

II) y2 + 20y + 91 = 0

 

3) I) 3x2 – 12x – 135 = 0

II) y2 – 19y + 90 = 0

 

4) I) x2 + 42x + 405=0

II) y2 + 45y + 506=0

 

5) I) x2 – 21x + 108 = 0

II) y2 – 27y + 176 = 0

Data Interpretation

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

Relationship cannot be established between x and y.

The given bar graph shows the percentage increment in the number of students on 2014 from 2013 and 2015 from 2014 in 5 different colleges A, B, C, D and E.

6) Find the total number of girl students from college A in 2013?

Statement I: Ratio of the number of boys to girls in college A in 2015 is 4:5 and the number of boys from A in 2013 is 80% of the number of boys from A in 2015.

Statement II: The number of girls from A in 2015 is 300.

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

7) What is the total number of students from B in 2013?

Statement I: If the number of girl students from B in 2013, 2014 and 2015 is 60%, 50% and 45% respectively and the average number of boys from B in 2013, 2014 and 2015 is 581.

Statement II: Difference between the total number of students from B in 2014 and 2015 is 480.

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

8) If sum of the total students from C in 2013 and 2015 is 640.

Quantity I: Ratio of the number of boys to girls from C in 2014 is 2: 3 and the total number of boy students from C in 2015 is 60% of the total number of girls from C in 2014. Find the total number of girls from C in 2015?

Quantity II: Ratio of the girls to boys from C in 2013 is 2: 3 and the ratio of the number of boys from C in 2014 to the number of girls from C in 2013 is 7: 5. What is the total number of girls from C in 2014?

a) Quantity I > Quantity II

b) Quantity I ≥ Quantity II

c) Quantity II > Quantity I

d) Quantity II ≥ Quantity I

e) Quantity I = Quantity II or Relation cannot be established

9) What is the average number of students from E in 2015 and 2013?

Statement I: Ratio of the number of boys from E in 2013, 2014 and 2015 is 2: 4:5 and the ratio of the girls from E in 2013, 2014 and 2015 is 3: 4: 2.

Statement II: Difference between the number of girls from E in 2014 and the number of boys from E in 2015 is 120.

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

10) Find the average number of girls from D in 2013, 2014 and 2015 together?

Statement I: Total number of students in 2013 from D is 200 more than that the number of students in 2013 from E. Ratio of the number of girls to boys from D in 2013 is 3:2.

Statement II: Ratio of the number of boys to girls from D from in 2014 is 5:7 and the number of girl students from D in 2015 is 90.

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

Answers :

Directions (1 – 5):

1) Answer: E

I) x2 – 40x + 391 = 0

(x – 17) (x – 23) = 0

x = 17, 23

II) y2 – 8y – 345 = 0

(y + 15) (y – 23) = 0

y = -15, 23

Relationship can’t be determined.

2) Answer: B

I) 2x2 + 28x + 98 = 0

2x2 + 14x + 14x + 98 = 0

2x(x + 7) + 14(x + 7) = 0

(2x + 14)(x + 7) = 0

x = -7, -7

II) y2 + 20y + 91 = 0

(y + 7) (y + 13) = 0

x = -7, -13

x ≥ y

3) Answer: D

I) 3x2 – 12x – 135 = 0

3x2 – 27x + 15x – 135 = 0

3x(x – 9) + 15(x – 9) = 0

(3x + 15)(x – 9) = 0

x = -5, 9

II) y2 – 19y + 90 = 0

(y – 10) (y – 9) = 0

y = 10, 9

x ≤ y

4) Answer: E

I) x2 + 42x + 405=0

(x + 15) (x + 27)=0

x = -15, -27

II) y2 + 45y + 506 = 0

(y + 22) (y + 23) = 0

y = -22, -23

Relationship cannot be established between x and y.

5) Answer: E

I) x2 – 21x + 108 = 0

(x – 9) (x – 12) = 0

x = 9, 12

II) y2 – 27y + 176 = 0

(y – 16) (y – 11) = 0

y = 16, 11

Relationship cannot be established between x and y.

Directions (6 – 10):

6) Answer: D

From statement I,

Total number of students from A in 2015 = 9x

Number of boys from A in 2015 = 4x

Number of girls from A in 2015 = 5x

Number of boys from A in 2013 = 80/100 * 4x = 16x/5

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

From statement II,

Number of girls from A in 2015 = 300

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

From I and II,

Number boys from A in 2015=4/5 * 300 = 240

Total number of students from A in 2015 = 9/5 * 300 = 540

Total number of students from A in 2013 = 540 * 100/125 * 100/120

= 360

Number of boys from A in 2013 = 80/100 * 240 = 192

Number of girls from A in 2013 = 360 – 192 = 168

7) Answer: C

From statement I,

Total number of students from B in 2013 = x

Total number of students from B in 2014 = 125x/100 = 5x/4

Total number of students from B in 2015 = 5x/4 * 115/100 = 23x/16

Number of boys from B in 2013 = x * 40/100 = 2x/5

Number of boys from B in 2014 = 5x/4 * 50/100 = 5x/8

Number of boys from B in 2015 = 55/100 * 23x/16 = 253x/320

Average of boys = 581

(2x/5 + 5x/8 + 253x/320) / 3 = 581

(128x + 200x + 253x/320) = 1743

x = 960

Total number of students from B in 2013 = 960

So, Statement I alone is sufficient to answer the question.

From statement II,

Total number of students from B in 2013 = x

Total number of students from B in 2014 = 125x/100 = 5x/4

Total number of students from B in 2015 = 5x/4 * 115/100 = 23x/16

23x/16 – 5x/4 = 480

3x/16 = 480

x = 2560

Total number of students from B in 2013 = 2560

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

8) Answer: A

Total number of students from C in 2013 = x

Total number of students from C in 2014 = x * 130/100 = 13x/10

Total number of students from C in 2015 = 13x/10 * 120/100 = 39x/25

x + 39x/25 = 640

64x = 640 * 25

x = 250

Total number students from C in 2014 = 13 * 250/10 = 325

Total number of students from C in 2015 = 39 * 250/25 = 390

From quantity I,

Number of girls from C in 2014 = 3/5 * 325 = 195

Number of boys from C in 2015 = 195 * 60/100 = 117

Number of girls from C in 2015 = 390 – 117 = 273

From quantity II,

Number of girls from C in 2013 = 2/5 * 250 = 100

Number of boys from C in 2014 = 7/5 * 100 = 140

Number of girls from C in 2014 = 325 – 140 = 185

Quantity I > quantity II

9) Answer: E

From statement I,

Boys from E in 2013, 2014 and 2015=2: 4: 5

Girls from E in 2013, 2014 and 2015=3: 4: 2

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

From statement II,

Difference between the number of girls from E in 2014 and the number of boys from E in 2015 is 120.

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

10) Answer: E

From statement I,

Number of students from D in 2013 = 200 + number of students from E in 2013

Ratio of the number of girls to boys from D in 2013 is 3:2.

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

From statement II,

Ratio of boys to girls from D in 2014 = 5: 7

Number of girls from E in 2015 = 90

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

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