Divisibility Questions and Answers

When we divide 3697 by 2, we get 1848 as the quotient and 1 as the remainder.

 

So 789 will be Quotient

The simple way is to sum all the digits, if the result is divisible by 3, the number is divisible by 3.

1 + 1 + 1 = 3

9 + 9 + 3 = 21

1 + 2 +5 = 8

9 + 9 + 9 = 27

All the numbers above are divisible by 3, except 8.

Therefore, 125 is not divisible by 3.

 

The LCM of 3, 5, and 10 is 30. 

Therefore option C is the correct one. 

Total number of prime numbers below 500 is 95.

When we exclude 2, 3, 5, 7, and 9, we get 91.

Numbers which are not divisible by 2, 3, 4, 5, 7, or 21 are

11 x (11, 13, 17, 19, 23, 29, 31, 37, 41, 43) which are 10.

13 x (13, 17, 19, 23, 29, 31, 37) which are 7.

17 x (17, 19, 23, 29) which are 4

19 x (19, 23) which are 2

Initially, 1 is also not divisible

Total = 91+10+7+4+2+1

= 115

Answer = 500 – 115 = 385

Therefore Option D is the correct one.

When we divide all the given options by 2, we get remainder only in the case of 21.  

All the remaining numbers generate 0 as the remainder. Thus the odd number in the given options is 21. 

Therefore Option A is the correct one. 

The quotient is 496, and the remainder is 0.

 

We already know that the sum of the first n numbers is \frac{B (B+1)}{2}

If B is an even number, the probability will be zero.

If B is odd, the probability is 1

If we consider the first B numbers, then the probability will be \frac{1}{2}

Therefore Option A is the correct one.

11 numbers are divisible between 1 and 100 by 9. 

25 numbers are divisible by 4 between 1 and 100. 

Therefore, total numbers = 36. 

Also, there are numbers which are divisible by both 4 and 9 and are counted twice.  

= 11 + 25 – 2 = 34. 

Therefore option A is the correct one. 

LCM of 12, 13, and 20 is 780. 

The least five digit number is 10000 

10000/780 = 12.82 

Therefore, the 13th multiple must be at least 5 digit number divisible by 12, 13, and 20. 

= 780 x 13 = 10140 

Hence Option B is the correct one. 

 

Largest Four digit Number is 9999


When Divide 9999 by 15 Remainder = 9

Largest Four digit Number which is divisible by 15 = 9999 - 9 = 9990

The number should be divisible by 3 and 4 to make it divisible by 12

last two digits(12) which is divisible by 4 so it is divisible by 4.

= 2 + 9 + 6 + x + 1 + 2 = 20 + x (if x =1, the number will be divisible by 3)

Therefore x =1.

Hence Option C is the correct one.