Dear Reader, Below are three practice questions on numbers.
Question 1
If N is a whole number, then N2(N2 – 1) is always divisible by one of the following:
a) 24 b) 12 c) 12- N d) none of these.
Answer : b) 12
Solution :
Assume N =2 , we get N2(N2-1) = 12. So N2(N2-1) is always divisible by 12.
When N is 3 or 4 or 5 , N2(N2-1) is divisible by 12 and 24 also. But where N is 6 or 9, N2(N2-1) is not divisible by 24. Another important point is 24 cannot be the choice because the resultant number N2(N2-1) is less than 24 when N = 2.. Thus, in all cases N2(N2– 1) values are divisible by 12 and not by 24 or 12-N.
Question 2
Ashwini asked Aishwarya a doubt on the following: “A 4 digit number is formed by repeating a 2 digit number such as 1313,4545, 6363 etc". Any number of this form is exactly divisible by:
a) 8 b) 11 c) 14 d) smallest 3-digit prime number
Answer : d) smallest 3-digit prime number (101)
Solution :
Smallest 3-digit prime number is 101.
1313 = 13 x 101
4545 = 45 x 101 etc. and so on.
Hence each such 4 digit number formed by repeating a 2 digit number is divisible by smallest 3-digit prime number 101.
Question 3
An intelligent boy told the number of birds in a different way as follows:
“ If one fifth of birds flew to jackfruit tree, one third flew to the mango tree , three times the difference of these two numbers flew to Banyan tree and one bird continued to fly about, attracted on each side by different trees, what was the total number of bees?
a) 15 b) 18 c) 19 d) 21.
Answer : a) 15.
Solution :
It is given that one fifth of birds flew to jackfruit tree, one third flew to the mango tree. This means that the number of birds should be divisible by 5 and 3. 15 is the only number among the options divisible by three and also five.