All Exams  >   SSC CGL  >   Quantitative Aptitude for SSC CGL  >   All Questions

All questions of Simplification & Approximation for SSC CGL Exam

7.8 + 5.4 x 8.2 = ?
  • a)
    52.08
  • b)
    108.24
  • c)
    48.05
  • d)
    102.05
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Solution for 7.8 + 5.4 × 8.2
We solve using the order of operations (BODMAS):
  1. First, perform the multiplication:
    5.4 × 8.2 = 44.28
  2. Next, add the result to 7.8:
    7.8 + 44.28 = 52.08
Correct Answer: A: 52.08

  • a)
    2 - √3
  • b)
    2 + √3
  • c)
    16 - √3
  • d)
    14 - √3
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Given expression:
[(2 + √3) / (2 - √3)] + [(2 - √3) / (2 + √3)] + [(√3 - 1) / (√3 + 1)]
  1. Simplify the first two terms:
    • The denominator simplifies to 1.
    • The numerator becomes 14.
    • Result: 14.
  2. Simplify the third term:
    • Rationalize the denominator to get 2 - √3.
  3. Add the results:
    • 14 + (2 - √3) = 14 - √3.
Correct Answer: C: 14 - √3

(?)3 x (55) ÷ 225 = 3000
  • a)
    6
  • b)
    8
  • c)
    5
  • d)
    9
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

 
To solve (?)³ × (5⁵) ÷ 225 = 3000, follow these steps:
  1. Rearrange the equation:
    (?)³ = (3000 × 225) ÷ 5⁵
  2. Calculate 5⁵:
    5⁵ = 3125
  3. Simplify the numerator:
    3000 × 225 = 675000
  4. Divide:
    675000 ÷ 3125 = 216
  5. Find the cube root of 216:
    √³(216) = 6
Correct Answer: A: 6

  • a)
    51
  • b)
    59
  • c)
    57
  • d)
    53
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Solution for ∛185193
To solve ∛185193, we find the cube root:
  • The cube root of 185193 is 57, since 57³ = 185193.
Correct Answer: C: 57

47.932 + 56 + 97.168 – 67 – 78.3 – 22.7
  • a)
    33    
  • b)
    32.1
  • c)
    33.1   
  • d)
    34.1
  • e)
    None
Correct answer is option 'C'. Can you explain this answer?

Expression:
( 47.932 + 56 + 97.168 - 67 - 78.3 - 22.7 )
Step 1: Add the positive terms:
( 47.932 + 56 + 97.168 = 201.1 )
Step 2: Add the negative terms:
( 67 + 78.3 + 22.7 = 168 )
Step 3: Subtract the sum of negative terms from the sum of positive terms:
( 201.1 - 168 = 33.1 )
Final Answer: The result of the expression is 33.1.

(169 – 144)½ ÷ (64 + 36)½ = ?
  • a)
    0.5
  • b)
    0.25
  • c)
    2.5
  • d)
    5
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

To solve the given expression:

1. Calculate the values inside the parentheses first: √(169 - 144 = 25) and √(64 + 36 = 100).
2. Now simplify the expression further: √25/√100 .
3. Calculate the square roots: 5/10
4. Finally, divide the two results: 0.5

Therefore, the correct answer is A: 0.5.

  • a)
    62
  • b)
    58
  • c)
    68
  • d)
    66
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?

Solution for ( ? )² / 4 + √1521 = 1063
To solve ( ? )² / 4 + √1521 = 1063, follow these steps:
  1. Calculate the square root of 1521:
    √1521 = 39
  2. Substitute into the equation and simplify:
    ( ? )² / 4 + 39 = 1063
    ( ? )² / 4 = 1063 - 39 = 1024
  3. Multiply by 4:
    ( ? )² = 1024 × 4 = 4096
  4. Take the square root:
    ? = √4096 = 64
Correct Answer: E: None of these

–224 + (–314) x (–9) = ?
  • a)
    2602
  • b)
    547
  • c)
    – 547
  • d)
    –2602
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Anaya Patel answered
Option (a) 2602 is correct. 
Explanation:- 
 
{ Given,   
-224 + ( - 314) * (-9) 
 According to BODMASS ; 
=>  -224 -314  * -9
=>  -224 +  2826
=>   2602

  • a)
    6241
  • b)
    6889
  • c)
    6561
  • d)
    5929
  • e)
    None of thes
Correct answer is option 'C'. Can you explain this answer?

Anaya Patel answered
C is the correct option. Solution- 
4028÷53=76
6156÷76=81
So the value needed is a square of 81 which is 6561.

  • a)
  • b)
  • c)
    4
  • d)
  • e)
    None of these
Correct answer is 'C'. Can you explain this answer?

To solve 82/3, follow these steps:
  1. Interpret the fractional exponent:
    82/3 = (∛8)2
  2. Find the cube root of 8:
    ∛8 = 2
  3. Square the result:
    2² = 4
Correct Answer: C: 4

  • a)
  • b)
  • c)
  • d)
  • e)
Correct answer is option 'C'. Can you explain this answer?

= we know,
(4-3+13-8)+(1/2 - 1/7 + 2/7 -1/4)
= 6 + 11/28

= option C 

856 x 567 = ?
  • a)
    487064
  • b)
    484218
  • c)
    482784
  • d)
    485352
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Sajal Bdw answered
An easy way (here) just multiply units digit of two number
6×7=42 so whatever the number will be it will have unit place 2 therefore the answer is D

(764 x ?) ÷ 250 = 382
  • a)
    135
  • b)
    125
  • c)
    115
  • d)
    145
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Solution:

Given equation:

(764 x ?) ÷ 250 = 382

Solving for ?:

(764 x ?) = 382 x 250

? = (382 x 250) / 764

? = 125

Therefore, the value of ? is 125.

So, the correct answer is B: 125.

The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the number.
  • a)
    42   
  • b)
    53  
  • c)
    17  
  • d)
    71  
  • e)
    None
Correct answer is option 'D'. Can you explain this answer?

Let the two-digit number be represented as 10a + b, where:
  • a is the tens digit.
  • b is the one digit.
According to the problem:
  1. The sum of the digits is 8:
    a+b=8
  2. When the digits are reversed, the number is decreased by 54. The number with reversed digits is 10b + a. So:
    10a+b−(10b+a)=54
    Simplifying this equation:
    10a+b−10b−a=54
    9a−9b=54
    a−b=6
Now, we have two equations:
  1. a+b=8
  2. a−b=6
Add these two equations:
(a+b)+(a−b)=8+6
2a = 14
a=7
Substitute a=7 into a+b=8:
7+b=8 , b = 1
So, the number is 10a+b=10×7+1=71
Answer: The number is 71.

36 * 1.75 + 24 * 3.25 = ? 
  • a)
    142
  • b)
    141
  • c)
    162
  • d)
    182
  • e)
    152
Correct answer is option 'B'. Can you explain this answer?

Sukamar Kumar answered
15Aug-2023 — Customer contact +91 824-843-8395-(complain customer service head Office number) +91 824.843.8395 call us now serious .

Directions: What approximate value will come in place of the question mark (?) in the following question
√785 + √729.50 = ?
  • a)
    52.50
  • b)
    55
  • c)
    57.50
  • d)
    60
Correct answer is option 'B'. Can you explain this answer?

Pranab Goyal answered
Understanding the Problem
To solve the expression √785 + √729.50, we need to approximate the square roots of both numbers.
Approximation of √785
- √785 is close to √784, which is exactly 28 (since 28 x 28 = 784).
- Thus, we can estimate √785 to be slightly more than 28, approximately around 28.03.
Approximation of √729.50
- √729 is exactly 27 (since 27 x 27 = 729).
- Since 729.50 is slightly greater than 729, we can estimate √729.50 to be slightly more than 27, approximately around 27.01.
Adding the Approximations
Now, we will add the approximated values:
- √785 ≈ 28.03
- √729.50 ≈ 27.01
So,
- 28.03 + 27.01 = 55.04
Conclusion
Rounding off 55.04 gives us approximately 55. Therefore, the answer to the equation √785 + √729.50 is closest to option 'B', which is 55.
This method of approximation allows us to quickly assess the problem without needing to calculate the exact square roots.

Find the number in the unit place in (321)321 x (325)326.
  • a)
    1   
  • b)
    5  
  • c)
    6   
  • d)
    8
  • e)
    None
Correct answer is option 'B'. Can you explain this answer?

Faizan Khan answered
321 raised to 321=1 in unit digit and any number ending in 5 raised to any number has always 5 as unit digit, so 1×5=5

Directions: What approximate value will come in place of the question mark (?) in the following question?
(49.97% of 881) + ? + (400% of 8.001) = 875
  • a)
    400
  • b)
    403
  • c)
    406
  • d)
    409
Correct answer is option 'B'. Can you explain this answer?

Pranab Goyal answered
Understanding the Problem
To find the value of '?', we need to solve the equation:
(49.97% of 881) + ? + (400% of 8.001) = 875
We will break it down step by step.
Calculating 49.97% of 881
- First, convert the percentage to a decimal: 49.97% = 0.4997
- Now calculate:
- 0.4997 * 881 = approximately 440
Calculating 400% of 8.001
- Convert the percentage to a decimal: 400% = 4
- Now calculate:
- 4 * 8.001 = approximately 32.004
Setting Up the Equation
Now, substituting the values we calculated into the equation:
440 + ? + 32.004 = 875
Simplifying the Equation
Combine the known values:
- 440 + 32.004 = approximately 472.004
Now, the equation looks like this:
472.004 + ? = 875
Finding '?'
Now isolate '?':
? = 875 - 472.004
- Calculating this gives us approximately:
- 875 - 472 = 403
Final Answer
Therefore, the approximate value of '?' is 403, which corresponds to option 'B'.

  • a)
    0.668
  • b)
    2.99
  • c)
    0.167
  • d)
    7
  • e)
    none of these
Correct answer is option 'B'. Can you explain this answer?

The given expression is:
(4.669 × 4.669 - 2.331 × 2.331) / ((4.669)² + (2.331)² - 4.669 × 4.662)
  1. Numerator:
    4.669 × 4.669 = 21.794
    2.331 × 2.331 = 5.433
    21.794 - 5.433 = 16.361
  2. Denominator:
    (4.669)² = 21.794
    (2.331)² = 5.433
    4.669 × 4.662 = 21.748
    21.794 + 5.433 - 21.748 = 5.479
  3. Final Calculation:
    16.361 / 5.479 ≈ 2.99
Answer: B: 2.99

  • a)
    6.9375   
  • b)
    4.2968  
  • c)
    2.1250   
  • d)
    2.0000
  • e)
    None
Correct answer is option 'A'. Can you explain this answer?

To solve the expression:
Step 1: Convert the mixed fraction to a decimal.
14   = 6.25)
Now, substitute (6.25) into the expression:
Expression: (6.25 + 0.25 + 0.75 - 0.3125)
Step 2: Calculate each operation:
  • (6.25 + 0.25 = 6.5)
  • (6.5 + 0.75 = 7.25)
  • (7.25 - 0.3125 = 6.9375)
Answer: a) 6.9375

Chapter doubts & questions for Simplification & Approximation - Quantitative Aptitude for SSC CGL 2025 is part of SSC CGL exam preparation. The chapters have been prepared according to the SSC CGL exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for SSC CGL 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Simplification & Approximation - Quantitative Aptitude for SSC CGL in English & Hindi are available as part of SSC CGL exam. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.

Top Courses SSC CGL