# How To Solve Number System Questions Quickly

## 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. ### 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

### 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

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### 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.

### 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.

### 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

### Question 6

6596 – ? = 6459 – 3357
Options

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

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

### 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.

### 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

### 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

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### One comment on “How To Solve Number System Questions Quickly”

• Asha Kanta

Excellent… 25