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Question 171

Other Govt. Exams 2023• Numerical Aptitude

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x2 – 11√3x + 90 = 0

II. y2 – 9√7y + 140 = 0

  1. AOption (a)

    x > y

  2. BOption (b)

    x < y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    x = y or relationship between x and y cannot be established.

View answer & explanation

Correct answer

Answer: (b)B.

x < y

Why this answer is correct

Calculations:

I. x2 – 11√3x + 90 = 0

⇒ x2 – 6√3x – 5√3x + 90 = 0

⇒ x(x – 6√3) – 5√3(x - 6√3) = 0

⇒ (x – 6√3) (x – 5√3) = 0

⇒ x = 6√3, 5√3

 

II. y2 – 9√7y + 140 = 0

⇒ y2 – 5√7y – 4√7y + 140 = 0

⇒ y(y - 5√7) – 4√7(y – 5√7) = 0

⇒ (y – 5√7) (y – 4√7) = 0

⇒ y = 5√7, 4√7

 

Comparison between x and y (via Tabulation):

Value of xValue of yRelation
5√35√7y > x
5√34√7y > x
6√35√7y > x
6√34√7y > x

∴ x < y

Important PointsThe value of √3 = 1.732 

The value of √7 = 2.645

Question 172

Other Govt. Exams 2023• Numerical Aptitude

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. 2x2 - 33x + 136 = 0

II. 2y2 - 37y + 171 = 0

  1. AOption (a)

    x > y

  2. BOption (b)

    x < y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    x = y or relationship between x and y cannot be established

View answer & explanation

Correct answer

Answer: (b)B.

x < y

Why this answer is correct

I. 2x2 - 33x + 136 = 0

⇒ 2x2 - 17x - 16x + 136 = 0

⇒ (x - 8) (2x - 17) = 0

⇒ x = 8, 17/2

II. 2y2 - 37y + 171 = 0

⇒ 2y2 - 19y - 18y + 171 = 0

⇒ (y - 9) (2y - 19) = 0

⇒ y = 9, 19/2

Value of xValue of yRelation
89x < y
819/2x < y
17/29x < y
17/219/2x < y

 

∴ x < y

Question 173

Other Govt. Exams 2023• Numerical Aptitude

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x = √529

II. y2 – 21y + 104 = 0

  1. AOption (a)

    x > y

  2. BOption (b)

    x < y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    x = y or relationship between x and y cannot be established.

View answer & explanation

Correct answer

Answer: (a)A.

x > y

Why this answer is correct

Calculation:

I. x = √529

⇒ x = 23

II. y2 – 21y + 104 = 0

⇒ y2 – 8y – 13y + 104 = 0

⇒ (y – 13) (y – 8) = 0

⇒ y – 13 = 0, and y – 8 = 0 

So, y = 13, and y = 8.

Value of xValue of yRelation
2313x > y
238x > y

∴ x > y

Kindly note that:  x = √529, which is the 1 st equation is a linear equation.

This means it will only have one solution. The solution will be positive.

If the equation was x2 = 529, then we will have 2 roots, as it is a quadratic equation. 

Keep this fact in mind as this will help us in solving this type of problem.

Question 174

Other Govt. Exams 2023• Numerical Aptitude

In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer-

I. x2 + 14x + 24 = 0

II. 9y2 – 4 = 0

  1. AOption (a)

    x > y

  2. BOption (b)

    y ≤ x

  3. COption (c)

    y ≥ x

  4. DOption (d)

    x < y

  5. EOption (e)

    Either x = y or Relation between x and y cannot be established.

View answer & explanation

Correct answer

Answer: (d)D.

x < y

Why this answer is correct

I. x2 + 14x + 24 = 0

⇒ x2 + 12x + 2x + 24 = 0

⇒ x(x + 2) + 12(x + 2) = 0

⇒ (x + 12)(x + 2) = 0

⇒ x = -12, x = -2

II. 9y2 – 4 = 0

⇒ 9y2 = 4

⇒ y = 2/3, y = -2/3

Value of xValue of yRelation
-122/3x < y
-22/3x < y
-12-2/3x < y
-2-2/3x < y

 

Hence, x < y

Question 175

Other Govt. Exams 2023• Numerical Aptitude

In the following question, two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

I. 6x + 16y = - 4

II. 8x + 36y = 2

  1. AOption (a)

    x > y

  2. BOption (b)

    x < y

  3. COption (c)

    x ≥ y

  4. DOption (d)

    x ≤ y

  5. EOption (e)

    x = y or relation cannot be established

View answer & explanation

Correct answer

Answer: (b)B.

x < y

Why this answer is correct

CALCULATION :

I. 6x + 16y = - 4

Multiplying on both sides by 4, we get,

⇒ 24x + 64y = - 16      ----(1)

II. 8x + 36y = 2

Multiplying on both sides by 3, we get,

⇒ 24x + 108y = 6      ----(2)

Subtracting equation 1 from 2, we get,

⇒ 44y = 22

⇒ y = 1/2      ----(3)

Substituting equation 3 in equation 1, we get,

⇒ 24x + 32 = - 16

⇒ 24x = - 48

⇒ x = - 2

∴ We can observe that x < y.

Question 176

Other Govt. Exams 2023• Reasoning Ability

Directions: Study the following information and answer the given questions.

Eight persons Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit are sitting around a circular table facing inside the centre, but not necessarily in the same order. Rahul is not sitting immediate left of Rohit. Tina is not immediate neighbor of Sonu. Two persons are sitting between Rohit and Priya. Gaurav sits second to the right of Pinku. Two persons are sitting between Rita and Rohit. Priya is not neighbor of Tina. Two persons are sitting between Priya and Sonu.

Who sits opposites to Priya?

  1. AOption (a)

    Rahul

  2. BOption (b)

    Sonu

  3. COption (c)

    Pinku

  4. DOption (d)

    Rohit

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (a)A.

Rahul

Why this answer is correct

Persons: Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit.

1). Two persons are sitting between Rohit and Priya.

2). Two persons are sitting between Rita and Rohit.

3). Two persons are sitting between Priya and Sonu.

4). Tina is not an immediate neighbor of Sonu.

5). Priya is not a neighbor of Tina.

6). Gaurav sits second to the right of Pinku.

7). Rahul is not immediate left of Rohit. ( from here Case 1 gets eliminated)

The final arrangements:

Hence, Rahul sits opposites to Priya.

Question 177

Other Govt. Exams 2023• Reasoning Ability

Directions: Study the following information and answer the given questions.

Eight persons Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit are sitting around a circular table facing inside the centre, but not necessarily in the same order. Rahul is not sitting immediate left of Rohit. Tina is not immediate neighbor of Sonu. Two persons are sitting between Rohit and Priya. Gaurav sits second to the right of Pinku. Two persons are sitting between Rita and Rohit. Priya is not neighbor of Tina. Two persons are sitting between Priya and Sonu.

Who sits third to the Right of Pinku?

  1. AOption (a)

    Sonu

  2. BOption (b)

    Rohit

  3. COption (c)

    Tina

  4. DOption (d)

    Rahul

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

Tina

Why this answer is correct

Persons: Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit.

1). Two persons are sitting between Rohit and Priya.

2). Two persons are sitting between Rita and Rohit.

3). Two persons are sitting between Priya and Sonu.

4). Tina is not an immediate neighbor of Sonu.

5). Priya is not a neighbor of Tina.

6). Gaurav sits second to the right of Pinku.

7). Rahul is not immediate left of Rohit. ( from here Case 1 gets eliminated)

The final arrangements:

Hence, Tina sits third to the right of Pinku.

Question 178

Other Govt. Exams 2023• Reasoning Ability

Directions: Study the following information and answer the given questions.

Eight persons Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit are sitting around a circular table facing inside the centre, but not necessarily in the same order. Rahul is not sitting immediate left of Rohit. Tina is not immediate neighbor of Sonu. Two persons are sitting between Rohit and Priya. Gaurav sits second to the right of Pinku. Two persons are sitting between Rita and Rohit. Priya is not neighbor of Tina. Two persons are sitting between Priya and Sonu.

How many persons sits between Sonu and Tina , when we move in anti-clockwise directions from Sonu?

  1. AOption (a)

    One

  2. BOption (b)

    Two

  3. COption (c)

    Three

  4. DOption (d)

    Four

  5. EOption (e)

    More than four

View answer & explanation

Correct answer

Answer: (d)D.

Four

Why this answer is correct

Persons: Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit.

1). Two persons are sitting between Rohit and Priya.

2). Two persons are sitting between Rita and Rohit.

3). Two persons are sitting between Priya and Sonu.

4). Tina is not an immediate neighbor of Sonu.

5). Priya is not a neighbor of Tina.

6). Gaurav sits second to the right of Pinku.

7). Rahul is not immediate left of Rohit. ( from here Case 1 gets eliminated)

The final arrangements:

Hence, Four persons sit between Sonu and Tina, when we move in an anticlockwise direction from Sonu.

Question 179

Other Govt. Exams 2023• Reasoning Ability

Directions: Study the following information and answer the given questions.

Eight persons Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit are sitting around a circular table facing inside the centre, but not necessarily in the same order. Rahul is not sitting immediate left of Rohit. Tina is not immediate neighbor of Sonu. Two persons are sitting between Rohit and Priya. Gaurav sits second to the right of Pinku. Two persons are sitting between Rita and Rohit. Priya is not neighbor of Tina. Two persons are sitting between Priya and Sonu.

If Priya change its position with Sonu, who sits immediate right of Sonu?

  1. AOption (a)

    Rita

  2. BOption (b)

    Pinku

  3. COption (c)

    Tina

  4. DOption (d)

    Gaurav

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (d)D.

Gaurav

Why this answer is correct

Persons: Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit.

1). Two persons are sitting between Rohit and Priya.

2). Two persons are sitting between Rita and Rohit.

3). Two persons are sitting between Priya and Sonu.

4). Tina is not an immediate neighbor of Sonu.

5). Priya is not a neighbor of Tina.

6). Gaurav sits second to the right of Pinku.

7). Rahul is not immediate left of Rohit. ( from here Case 1 gets eliminated)

The final arrangements:

After changing of position the new arrangements is

 

Hence, After changing positions Gaurav sits immediate right of Sonu.

Question 180

Other Govt. Exams 2023• Reasoning Ability

Directions: Study the following information and answer the given questions.

Eight persons Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit are sitting around a circular table facing inside the centre, but not necessarily in the same order. Rahul is not sitting immediate left of Rohit. Tina is not immediate neighbor of Sonu. Two persons are sitting between Rohit and Priya. Gaurav sits second to the right of Pinku. Two persons are sitting between Rita and Rohit. Priya is not neighbor of Tina. Two persons are sitting between Priya and Sonu.

Who among the following is the immediate neighbors of Tina?

  1. AOption (a)

    Rohit

  2. BOption (b)

    Sonu

  3. COption (c)

    Gaurav

  4. DOption (d)

    Both Rohit and Gaurav

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (d)D.

Both Rohit and Gaurav

Why this answer is correct

Persons: Rita, Tina, Sonu, Pinku, Rahul, Priya, Gaurav, and Rohit.

1). Two persons are sitting between Rohit and Priya.

2). Two persons are sitting between Rita and Rohit.

3). Two persons are sitting between Priya and Sonu.

4). Tina is not an immediate neighbor of Sonu.

5). Priya is not a neighbor of Tina.

6). Gaurav sits second to the right of Pinku.

7). Rahul is not immediate left of Rohit. ( from here Case 1 gets eliminated)

The final arrangements:

Hence, Both Rohit and Gaurav are the immediate neighbors of Tina.

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