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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
Â
2) I) 2x2 + 28x + 98 = 0
II) y2 + 20y + 91 = 0
Â
3) I) 3x2 – 12x – 135 = 0
II) y2 – 19y + 90 = 0
Â
4) I) x2 + 42x + 405=0
II) y2 + 45y + 506=0
Â
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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