When a positive integer ‘n’ is divided by 12, the remainder is 5. What will be the remainder if 8n2 + 7 is divided by 12 ?
a) 2
b) 3
c) 4
d) 5
b is the correct option
Ques 2 Number System
How many numbers between 1000 and 5000 are exactly divisible by 225?
a) 12
b) 14
c) 15
d) 18
d is the correct option
The first number divisible by 225 between 1000 and 5000 is 1125 and the last number is 4950. The difference between these two numbers is 4950 - 1125 = 3825. The number of multiples of 225 that are less than 3825 is 3825 / 225 = 17. Therefore, there are 17 + 1 = 18 numbers between 1000 and 5000 that are exactly divisible by 225.
Here is the solution in mathematical form:
Number of multiples of 225 between 1000 and 5000 = (5000 - 1000) / 225 + 1 = 18.
Ques 3 Number System
The sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them?
a) 24
b) 25
c) 26
d) 27
d is the correct option
Ques 4 Number System
The HCF of two numbers is 12. Which one of the following can never be their LCM.?
a) 24
b) 60
c) 90
d) 84
c is the correct option
The HCF of two numbers is the highest common factor of the two numbers. The LCM of two numbers is the lowest common multiple of the two numbers.
Since the HCF of the two numbers is 12, the LCM must be a multiple of 12.
Of the given options, only 90 is not a multiple of 12. Therefore, the LCM of the two numbers cannot be 90.
Therefore, the answer is 90.