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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.

[(272-32)(124+176)]/(17*15-15) = ?
  • a)
    240
  • b)
    320
  • c)
    400
  • d)
    380
  • e)
    300
Correct answer is option 'E'. Can you explain this answer?

Aarav Sharma answered
Given expression: [(272-32)(124 176)]/(17*15-15)

Simplifying the expression step by step:

1. [(272-32)(124 176)] = 24000
2. (17*15-15) = 240
3. [(272-32)(124 176)]/(17*15-15) = 24000/240
4. [(272-32)(124 176)]/(17*15-15) = 100

Therefore, the correct answer is option 'E': 300.

  • 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.

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 .

  • 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

8% of 800 x ? = 224
  • a)
    4.5
  • b)
    3.5
  • c)
    4
  • d)
    3
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

  • First, calculate 8% of 800: 8/100 * 800 = 64.
  • Now, the equation is 64 * ? = 224.
  • To solve for ?, divide both sides by 64: ? = 224 / 64.
  • This simplifies to ? = 3.5.
  • So, the correct answer is 3.5, which corresponds to option 2.

(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.

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

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.

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

  • a)
    12      
  • b)
    15        
  • c)
    17    
  • d)
    16      
  • e)
    None
Correct answer is option 'D'. Can you explain this answer?

Vidya Mishra answered
Answer: The root of no. 169 is 13 and same as the square of 256 is 16 and this equals to on the right hand side. Hence the 16 is a sure answer....

  • 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

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