**Number System Questions with Solution:** Hey Guys, Do you know, the number system questions are one of the cool problems in the Aptitude section of Mathematics. You just have to add, substract, multiply or divide one number with another number. I think you are very much aquented with the number system problems. So lets discuss different problems of number system with their solutions.

## Number System Questions with Solutions

**Q.1 What will be the solution of 34598205 × 999=?**

(A) 34563606747

(B) 34563606795

(C) 34563606022

(D) 34563444222

**Answer: (B) 34563606795**

**Solution:**Here we have two process to solve this question. First way we can multiply 34598205 with 999 which will be lengthy. So we have to follow the second method i.e:

34598205 × ( 1000 - 1 )

=34598205000 - 34598205

= 34563606795

**Q.2 What is the value of 998 × 112 + 998 × 88= ?**

(A) 199600

(B) 156666

(C) 456221

(D) 196632

**Answer: (A) 199600**

**Tips: **To solve this question we have to use distributive law:

**Solution: ** 998 × 112 + 998 × 88= 998 × ( 112 + 88) =998 × 200 = 199600

**Related Topics:**

**Q.3 What is the value of **

**742 × 742 + 258 × 258 + 2 × 742 × 258= ?**

(A) 10000000

(B) 45668222

(C) 1000000

(D) 4522588

**Answer: (C) 1000000**

**Tips: **Use ( a + b )²= a² + b² + 2ab

**Solution: **742 × 742 + 258 × 258 + 2 × 742 × 258= (742)² + (258)² + 2 × 742 × 258= (742 + 258)²=1000²=1000000

**Q.4 Find the value of $ for which 236$62 is divisible by 3 and must be an odd number?**

(A) 3

(B) 5

(C) 7

(D) 9

**Answer: (D) 9**

**Tips: **Use the divisible formula for 3 i.e A number is divisible by 3 if the sum of all the digit of the number is divisible by 3.

**Solution: **Sum of the given number 2 + 3 + 6 + 6 + 2= 18

So possible answer is 2,

**Q.5 Weather 876744 is divisible by 88?**

(A) Yes

(B) No

**Answer: (A) Yes**

**Tips: **Use divisible formula of 11 and 8.

**Solution: **88= 11 × 8

- Sum of digits at odd place - Sum of digits at even place = ( 8 + 6 + 4) - ( 7 + 7 + 4)= 18 - 18= 0 which is divisible by 11 So 876744 is divisible by 11
- Last 3 digit of 876744 is 744 which is divisible by 8, so 876744 is divible by 8.

So, 876744 is divisible by 88 because 876744 is divisible by both 11 and 8.

**Q.6 What will be the unit digit in the multiplication of (5227)³¹³ ×(91)³²¹?**

(A) 1

(B) 3

(C) 7

(D) 9

**Answer: (C) 7**

**Solution: **We have to calculate the unit digit in (5227)³¹³ × (91)³²¹

As we know 7^{4 }having 1 as unit digit and (5227)³¹³ 's unit digit can be calculated as per the power of 7 and (91)³²¹ unit digit can be calculated by the help of 1.

So we can write (7)³¹³× (1)³²¹=(7)³¹² × 7 × (1)³²¹= ((7)^{4})^{78} × 7 × 1

Hence our required unit digit = ( 1 × 7 × 1) = 7

**Q.7 What is the minimum number we have to add with 2019 to obtain a number which is completely divisible by 11?**

(A) 12

(B) 5

(C) 6

(D) 4

**Answer: (B) 5**

**Tips: **Use formula Required Number = Divisor - Remainder

**Solution: **

** So our Required Number= 11 - 6 = 5**

**Q.8 What is the minimum number we have to subtract with 2019 to obtain a number that is completely divisible by 11?**

(A) 12

(B) 5

(C) 6

(D) 4

**Answer: (B) 5**

**Tips: **Use formula Required Number =Remainder

**Solution:**

** So Our Required Number=6**

**Q.9 What will be the sum of 1² + 2 ² + 3² + 4² + 5²+ ……..+ 890² ?**

(A) 396494

(B) 396495

(C) 396496

(D) 396497

**Answer: (B) 705761100**

**Tips: **Use the series formula ** 1² + 2 ² + 3² + 4² + 5²+ ........+ n²= ½n(n+1) (2n + 1)**

**Solution: **In 1² + 2 ² + 3² + 4² + 5²+ ........+ 890² here n= 890

So as per the formula we have: ½ × 890(890+1) (2×890 + 1) = 445 × 891 × 1780= 705761100

**Q.10 What will be the sum of 1³ + 2³ + 3³ + 4³ + 5³+ ……..+18³ ?**

(A) 705761101

(B) 128608721

(C) 128608722

(D) 12860855

**Answer: (C) 128608722**

**Tips: **Use the series formula ** 1³ + 2³ + 3³ + 4³ + 5³+ ........+ n³= ½n²(n+1)²**

**Solution: **In 1**³** + 2 **³** + 3**³** + 4**³** + 5**³**+ ........+ 18**³** here n= 18

So as per the formula we have: ½ × 18²(890+1)²= 162 × 793881= 128608722

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