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Question 1 of 10

1 points

Category: Quantitative Aptitude

Q (1-5) Quadratic Equation

Mark A if x>y
Mark B if y>x
Mark C if x≥y
Mark D if y≥x
Mark E in all other cases

Equation 1: 7x^{2} + 6x + 19 = 20
Equation 2: 3y^{2 } – 5y + 8 = 6

Correct
Explanation:
Equation 1: 7x^{2} + 6x + 19 = 20
⇒ 7x^{2 } + 6x – 1 = 0
⇒ 7x^{2 } + 7x – x – 1 = 0
⇒ 7x (x + 1) –1 (x + 1) = 0
⇒ (7x –1) (x + 1) = 0
∴ x = 1/7, –1

Equation 2:
3y^{2 } – 5y + 8 = 6
⇒ 3y^{2} – 5y + 2 = 0
⇒ 3y^{2} – 3y – 2y + 2= 0
⇒ 3y (y –1) – 2(y –1) = 0
⇒ (3y –2) (y – 1) = 0
⇒y = 2/3, 1
∴ x <y

Incorrect
Explanation:
Equation 1: 7x^{2} + 6x + 19 = 20
⇒ 7x^{2 } + 6x – 1 = 0
⇒ 7x^{2 } + 7x – x – 1 = 0
⇒ 7x (x + 1) –1 (x + 1) = 0
⇒ (7x –1) (x + 1) = 0
∴ x = 1/7, –1

Equation 2:
3y^{2 } – 5y + 8 = 6
⇒ 3y^{2} – 5y + 2 = 0
⇒ 3y^{2} – 3y – 2y + 2= 0
⇒ 3y (y –1) – 2(y –1) = 0
⇒ (3y –2) (y – 1) = 0
⇒y = 2/3, 1
∴ x <y

Question 2 of 10

1 points

Category: Quantitative Aptitude

Q (1-5) Quadratic Equation

Mark A if x>y
Mark B if y>x
Mark C if x≥y
Mark D if y≥x
Mark E in all other cases

Equation 1: x^{2} – 20x + 76 = 3x
Equation 2: y^{2} –25y + 399= 15y

Correct
Explanation:

Equation 1:
x^{2} – 20x + 76 = 3x
⇒ x^{2 } – 23x + 76 = 0
⇒ x^{2} – 19x – 4x + 76 = 0
⇒x(x – 19) – 4 ( x – 19) = 0
⇒ (x – 4) (x – 19) = 0
⇒x = 4, 19

Equation 2:
y^{2} –25y + 399= 15y
⇒y^{2} -40y + 399 = 0
⇒ y^{2} – 21y – 19y + 399 = 0
⇒ y(y –21) – 19 ( y – 21) = 0
⇒ (y – 19) (y – 21) = 0
⇒y = 19, 21
∴ y ≥ x

Incorrect
Explanation:

Equation 1:
x^{2} – 20x + 76 = 3x
⇒ x^{2 } – 23x + 76 = 0
⇒ x^{2} – 19x – 4x + 76 = 0
⇒x(x – 19) – 4 ( x – 19) = 0
⇒ (x – 4) (x – 19) = 0
⇒x = 4, 19

Equation 2:
y^{2} –25y + 399= 15y
⇒y^{2} -40y + 399 = 0
⇒ y^{2} – 21y – 19y + 399 = 0
⇒ y(y –21) – 19 ( y – 21) = 0
⇒ (y – 19) (y – 21) = 0
⇒y = 19, 21
∴ y ≥ x

Question 3 of 10

1 points

Category: Quantitative Aptitude

Q (1-5) Quadratic Equation

Mark A if x>y
Mark B if y>x
Mark C if x≥y
Mark D if y≥x
Mark E in all other cases

Equation 1: 4x^{2} -8x = 4(x + 4)
Equation 2: 16y^{2} + 1 = 8y

Correct
Equation 1:
4x^{2} -8x = 4(x + 4)
⟹x^{2} -2x – x – 4 = 0
⟹x^{2} -3x – 4= 0
⟹x^{2} -4x + x – 4 = 0
⟹ x (x – 4) + 1(x – 4) = 0
⟹x = -1, 4

Equation 2:
16y^{2} + 1 = 8y
⟹16y^{2} – 8y + 1 = 0
⟹16y^{2} – 4y – 4y + 1 = 0
⟹4y (4y – 1) – 1(4y -1) = 0
y=1/4,1/4
∴No relationship

Incorrect
Equation 1:
4x^{2} -8x = 4(x + 4)
⟹x^{2} -2x – x – 4 = 0
⟹x^{2} -3x – 4= 0
⟹x^{2} -4x + x – 4 = 0
⟹ x (x – 4) + 1(x – 4) = 0
⟹x = -1, 4

Equation 2:
16y^{2} + 1 = 8y
⟹16y^{2} – 8y + 1 = 0
⟹16y^{2} – 4y – 4y + 1 = 0
⟹4y (4y – 1) – 1(4y -1) = 0
y=1/4,1/4
∴No relationship

Question 4 of 10

1 points

Category: Quantitative Aptitude

Q (1-5) Quadratic Equation

Mark A if x>y
Mark B if y>x
Mark C if x≥y
Mark D if y≥x
Mark E in all other cases

Equation1 : x^{2} + 68x – 1053 = 0
Equation2 : y^{2} –33y +272 = 0

Correct
Explanation:
I. x^{2} +81x-13x -1053 =0
x(x+81)-13(x+81) =0
(x-13)(x+81)=0
x=-81,13

II. y^{2} – 16y – 17y +272 = 0
y(y – 16) –17(y –16) = 0
(y-16)(y-17)=0
y=17,16

Incorrect
Explanation:
I. x^{2} +81x-13x -1053 =0
x(x+81)-13(x+81) =0
(x-13)(x+81)=0
x=-81,13

II. y^{2} – 16y – 17y +272 = 0
y(y – 16) –17(y –16) = 0
(y-16)(y-17)=0
y=17,16

Question 5 of 10

1 points

Category: Quantitative Aptitude

Q (1-5) Quadratic Equation

Mark A if x>y
Mark B if y>x
Mark C if x≥y
Mark D if y≥x
Mark E in all other cases

Equation 1: x^{2} – 3x – 18 = 0
Equation 1: 3y^{2 } + 19y + 30 = 0

Correct
I.x^{2} – 3x – 18 = 0
x^{2} – 6x + 3x -18 = 0
x (x-6) + 3(x -6) = 0
(x+3) (x-6) = 0
x = -3, 6

II.3y^{2 } + 19y + 30 = 0
3y^{2} +10y + 9y + 30 = 0
y(3y + 10) + 3(3y + 10)
(y + 3)(3y + 10) = 0
y = -3, -10/3

Incorrect
I.x^{2} – 3x – 18 = 0
x^{2} – 6x + 3x -18 = 0
x (x-6) + 3(x -6) = 0
(x+3) (x-6) = 0
x = -3, 6

II.3y^{2 } + 19y + 30 = 0
3y^{2} +10y + 9y + 30 = 0
y(3y + 10) + 3(3y + 10)
(y + 3)(3y + 10) = 0
y = -3, -10/3

Question 6 of 10

1 points

Category: Quantitative Aptitude

If equal number of Mains tests were conducted by site A in month of April and June the number of tests conducted in June is?

Correct
Explanation:

Site
A
B
C
D
PRE
MAINS
PRE
MAINS
PRE
MAINS
PRE
MAINS
March
15
20
17
25
37
32
29
18
April
30
25
40
29
38
18
27
28
May
25
30
23
32
33
10
40
38
June
10
25
38
17
20
20
33
20
July
0
50
12
34
30
33
17
20
August
20
0
18
15
17
37
50
30
100
150
148
152
175
150
196
154

Incorrect
Explanation:

Site
A
B
C
D
PRE
MAINS
PRE
MAINS
PRE
MAINS
PRE
MAINS
March
15
20
17
25
37
32
29
18
April
30
25
40
29
38
18
27
28
May
25
30
23
32
33
10
40
38
June
10
25
38
17
20
20
33
20
July
0
50
12
34
30
33
17
20
August
20
0
18
15
17
37
50
30
100
150
148
152
175
150
196
154

Question 7 of 10

1 points

Category: Quantitative Aptitude

How much more percent is pre exams conducted by C in month of May than pre exams conducted by D in July?

Correct
Explanation:
(33-17)/17*100=94.11

Incorrect
Explanation:
(33-17)/17*100=94.11

Question 8 of 10

1 points

Category: Quantitative Aptitude

What are the total exams conducted by all sites in the month of April?

Question 9 of 10

1 points

Category: Quantitative Aptitude

Which website conducts second highest number of PRE exams?

Question 10 of 10

1 points

Category: Quantitative Aptitude

Which website conducts lowest number of mains Exam?

Correct
Explanation:
Both A and C

Incorrect
Explanation:
Both A and C

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