How To Solve Number System Questions Quickly

March 6, 2024

How to solve number system easily

Number System is one of the most common and important topics in Quantitative Aptitude. Here we are providing you an idea about How to Solve Number System Questions Quickly.

Solve Number System Questions

Important Formulas to solve Number System quickly

1. (a + b)(a – b) = (a² – b²)

2. (a + b)² = (a² + b² + 2ab)

3. (a – b)² = (a² + b² – 2ab)

4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

5. (a³ + b³) = (a + b)(a² – ab + b²)

6.(a³ – b³) = (a – b)(a² + ab + b²)

7. (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)

8. when a + b + c = 0, then a³ + b³ + c³ = 3abc

How To Solve Number System Questions Quickly Type – 1

Question 1.

34567 x 9999 =?
Options.

A. 345635432
B. 345634533
C. 345635433
D. 345635343

Solution:

34567 x 9999 = 34567 x (10000 – 1)
34567 x 9999 = 34567 x (10000) – 34567 x 1
34567 x 9999 = 345670000 – 34567
34567 x 9999 = 345635433

Correct option C

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How to Solve Number System Questions Quickly Type – 2

Question 2. 

The smallest 3 digit prime number is:
Options 

A. 100
B. 103
C. 105
D. 101

Solution:

The smallest three digit number is 100 but it is not a prime number. The next number is 101 and it is a prime number because it is divisible by 1 and itself only. Therefore, 101 is the smallest 3 digit prime number.

Correct option: D

Question 3.

Choose the terminating decimal

Options

A. 99.5555
B. 3.777
C. 0.6
D. 0.454545454545

Solution:

A terminating decimal is a decimal that ends after few repetitions after decimal point.
Correct option: C

Question 4.

Which of the following is not the Natural number?

Options 

A. 1
B. 3
C. 0
D. 5

Solution:

All counting numbers from 1 to infinity are natural numbers.

Correct option: C

Question 5.

Choose the non- terminating decimal?
Options

A. \frac{4}{45}
B. \frac{5}{8}
C. \frac{1}{4}
D. \frac{9}{1280}

Solution:

\frac{4}{45} = 0.08888…
\frac{5}{8} = 0.625
\frac{1}{4}= 0.25
\frac{9}{1280}= 0.00703125

Correct option: A

How to Solve Number System Questions Quickly Type – 3

Question 6

6596 – ? = 6459 – 3357
Options

A. 3949
B. 3494
C. 3102
D. 3499

Solution:

6596 – x = 3102
-x = 3102 – 6596
– x = – 3494
x = 3494

Correct option: B

Question 7

Which one of the following cannot be the square of natural number?
Options

A. 7225
B. 3136
C. 8100
D. 3457

Solution:

7225 = (85)2
3136 = (56)2
8100 = (90)2
3457 is not the square of any natural number as square of any natural number never ends with 7.

Correct option: D

Question 8

What is the unit digit in the product (365 x 659 x 771)?
Options 

A. 1
B. 2
C. 3
D. 4

Solution:

Unit digit in 34 = 1 
So, Unit digit in (34)16 = 1
Unit digit in 365 = 365 = (34)16 x 31 = (1 x 3) = 3
Unit digit in 659 = 6
Unit digit in 74 = 1

So, Unit digit in(74)17 is 1
Unit digit in 771 = (74)17 x 73 = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4

Correct option: D

Question 9

117 * 117 + 83 * 83 = ?

Options

A. 40578
B. 20578
C. 31090
D. 34567

Solution:

(117)² + (83)² = (100 + 17)² + (100 – 17)²
= 2 *[ (100)² + (17)²]
= 2 * (10000 + 289)
= 2 * 10289
= 20578

Correct option: B

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