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Question 251

LIC Assistant 2022• Quantitative 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 – 7x + 12 = 0

II. 2y2 – 19y + 44 = 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 no relationship can be obtained

View answer & explanation

Correct answer

Answer: (b)B.

x ≤ y

Why this answer is correct

Here,

⇒ P(x) = x2 - 7x + 12 = 0

⇒ P(y) = 2y2 - 19y + 44 = 0

Factorization of P(x) and P(y);

⇒ P(x) = x2 - 3x - 4x + 12 = 0

⇒ x(x - 3) - 4(x - 3) = 0

⇒ (x - 3) (x - 4) = 0

⇒ x = 3 or x = 4

⇒ P(y) = 2y2 - 8y - 11y + 44 = 0

⇒ 2y(y - 4) - 11(y - 4) = 0

⇒ (y - 4)(2y - 11) = 0

⇒ y = 4 or y = 11/2

⇒ x ≤ y

Question 252

LIC Assistant 2022• Quantitative Aptitude

In the following question two equations numbered I and II are given. You have to solve both the equations and give the answer:

I. 3x2 - 13x + 12 = 0

II. 2y2 - 15y + 28 = 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 no relationship can be obtained

View answer & explanation

Correct answer

Answer: (a)A.

x < y

Why this answer is correct

Here,

P(x) = 3x2 - 13x + 12 = 0

P(y) = 2y2 - 15y + 28 = 0

Factorization of P(x) and P(y);

⇒ P(x) = 3x2 - 9x - 4x + 12 = 0

⇒ 3x(x - 3) - 4(x - 3) = 0

⇒ (x - 3) (3x - 4) = 0

⇒ x = 3 or x = 4/3

⇒ P(y) = 2y2 - 8y - 7y + 28 = 0

⇒ 2y(y - 4) - 7(y - 4) = 0

⇒ (y - 4)(2y - 7) = 0

⇒ y = 4 or y = 7/2

Here, x < y

∴ Option 1 is the answer

Question 253

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

For disc D, what is the respective ratio of used space to the available space?

  1. AOption (a)

    2:1

  2. BOption (b)

    3:1

  3. COption (c)

    1:2

  4. DOption (d)

    1:3

  5. EOption (e)

    2:3

View answer & explanation

Correct answer

Answer: (c)C.

1:2

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

Required ratio = 50: 100

⇒ 1:2

∴ The correct answer is 1:2.

Question 254

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

For disc A, the total space available is how much more or less than that of disc D?

  1. AOption (a)

    25% more

  2. BOption (b)

    25% less

  3. COption (c)

    35% more

  4. DOption (d)

    40% more

  5. EOption (e)

    75% less

View answer & explanation

Correct answer

Answer: (b)B.

25% less

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

Required % = [(100 - 75)/100] × 100

⇒ 25% less

∴ The correct answer is 25% less.

Question 255

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

If another Disc E, has 20% more total storage than Disc C, and total used space in Disc E is same as DISC C, Then find out the available space in Disc E?

  1. AOption (a)

    70 GB

  2. BOption (b)

    60 GB

  3. COption (c)

    80 GB

  4. DOption (d)

    90 GB

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (c)C.

80 GB

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

 

Total storage in the disc E = 120% of 125

⇒ 150 GB

Total used space in the disc E = 70 GB

Total available space in the disc E = 150 - 70 = 80 GB

∴ The correct answer is 80 GB.

Question 256

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

which of the following option has maximum available space?

  1. AOption (a)

    Disk (A+C)

  2. BOption (b)

    Disk (A+B)

  3. COption (c)

    Disk (D+C)

  4. DOption (d)

    Disk (B+D)

  5. EOption (e)

    Disk (B+C)

View answer & explanation

Correct answer

Answer: (d)D.

Disk (B+D)

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

Available space in Disk (A+C) = 75 + 55 = 130

Available space in Disk (A+B) = 75 + 70 = 145

Available space in Disk (D+C) = 100 + 55 = 155

Available space in Disk (B+D) = 70 + 100 = 170

Available space in Disk (B+C) = 70 + 55 = 125

Here, Disk (B+D) has maximum available space

∴ The correct answer is Disk (B+D).

Question 257

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

Total used space in Disc B is how much percentage of the total used space in Disc A and disc D?

  1. AOption (a)

    20%

  2. BOption (b)

    30%

  3. COption (c)

    40%

  4. DOption (d)

    50%

  5. EOption (e)

    None of these

View answer & explanation

Correct answer

Answer: (b)B.

30%

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

 

Required % = [30/(50+50)] × 100 

⇒ 30%

∴ The correct answer is 30%.

Question 258

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

Find the percentage of total used space in Disc C with respect to total available space in Disc C?

  1. AOption (a)

    120.27%

  2. BOption (b)

    110.27%

  3. COption (c)

    125.27%

  4. DOption (d)

    127.27%

  5. EOption (e)

    130.27%

View answer & explanation

Correct answer

Answer: (d)D.

127.27%

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

Required % = [70/55] × 100 

⇒ 127.27%

∴ The correct answer is 127.27%.

Question 259

LIC Assistant 2022• Quantitative Aptitude

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

Pie chart 1 shows the percentage distribution of total storage in four disc A, B, C, and D respectively.

Pie chart 2 shows the percentage distribution of total used space in four disc A, B, C and D respectively.

Find the difference between the sum of total storage in Disc B and Disc D to the sum of disc A and disc C?

  1. AOption (a)

    0 GB

  2. BOption (b)

    5 GB

  3. COption (c)

    15 GB

  4. DOption (d)

    10 GB

  5. EOption (e)

    20 GB

View answer & explanation

Correct answer

Answer: (a)A.

0 GB

Why this answer is correct

From the data given in the pie chart, we have:

DiskTotal storage in the disc (500 GB)Total used space in the disc (200 GB)Total available space in the disc
A25% of 500 = 12525% of 200 = 50125 - 50 = 75
B20% of 500 = 10015% of 200 = 30100 - 30 = 70
C25% of 500 = 12535% of 200 = 70125 - 70 = 55
D30% of 500 = 15025% of 200 = 50150 - 50 = 100
Total500200300

Required difference = (100 + 150) - (125 + 125) = 0 GB

∴ The correct answer is 0 GB.

Question 260

LIC Assistant 2022• Quantitative Aptitude

Pipe A fills twice as fast as pipe B and pipe B fills twice as fast as pipe C. Pipe C can fill a tank in 20 hours. In how many hours will the tank fill if all the pipes are opened?

  1. AOption (a)

    \(2\frac{5}{7};{\text{hr}}\)

  2. BOption (b)

    \(3\frac{6}{7};{\text{hr}}\)

  3. COption (c)

    \(2\frac{6}{14};{\text{hr}}\)

  4. DOption (d)

    \(2\frac{6}{7};{\text{hr}}\)

  5. EOption (e)

    \(4\frac{6}{7};{\text{hr}}\)

View answer & explanation

Correct answer

Answer: (d)D.

\(2\frac{6}{7};{\text{hr}}\)

Why this answer is correct

Shortcut Trick

Ratio of efficiencies of Pipe A : Pipe B : Pipe C is 4 : 2 : 1.

Total Work = Efficiency of C × Time of C = 1 × 20 = 20 units.

Combined Efficiency = 4 + 2 + 1 = 7 units/hr.

Time Taken = 20 ÷ 7 = 2(6/7) hr.

∴ The correct answer is 2(6/7) hr.

Alternate Method

Given:

Time taken by Pipe C = 20 hours.

Efficiency of Pipe B = 2 × Efficiency of Pipe C.

Efficiency of Pipe A = 2 × Efficiency of Pipe B.

Formula Used:

Total Work = Efficiency × Time

PersonEfficiency (Ratio)Total WorkTime (hr)
Pipe C120 units20
Pipe B210
Pipe A45

Calculations:

⇒ Efficiency of Pipe C = 1 unit/hr

⇒ Efficiency of Pipe B = 2 × 1 = 2 units/hr

⇒ Efficiency of Pipe A = 2 × 2 = 4 units/hr

⇒ Total capacity of tank = 20 × 1 = 20 units

⇒ Combined efficiency of (A + B + C) = 4 + 2 + 1 = 7 units/hr

⇒ Total time required = 20 ÷ 7 hours

⇒ Time = 2(6/7) hours

∴ The correct answer is 2(6/7) hr.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If efficiency ratio is x:y, then time ratio is y:x.

Pipes and Cisterns

Inlet pipes have positive efficiency while outlet/leakage pipes have negative efficiency in calculations.

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