# Number Divisibility

Last Updated : 27 Sep, 2023

 Question 1

There is bag of lots of integers from 1 to 10000, but you can only pick the numbers that are of 3-digit and also divisible by 3. What maximum sum of numbers you can pick.

 165150 1600843 168132420 165322501

Question 1-Explanation:
```All 3 digit numbers divisible by 3 are :
102, 105, 108, 111, ..., 999.

This is an A.P. with first element \'a\' as
102 and difference  \'d\' as 3.

Let it contains n terms. Then,
102 + (n - 1) x 3 = 999
102 + 3n-3 = 999
3n = 900 or n = 300
Sum of AP = n/2 [2*a  + (n-1)*d]
Required sum = 300/2[2*102 + 299*3] = 165150. ```
 Question 2
Which of Following is not divisible from 4 ?
 546702 556824 367312 467536

Question 2-Explanation:
If last 2 digits are divisible by 4, then number is also divisible by 4.
```In case of 546702 last 2 digits are 02 (x)
In case of 556824 last 2 digits are 24 (/)
In case of 367312 last 2 digits are 12 (/)
In case of 467536 last 2 digits are 36 (/) ```
 Question 3
What should be the value of * in 985*865, if number is divisible by 9?
 6 5 4 0

Question 3-Explanation:
If a number is divisible by 9, the sum of digits is also divisible by 9
```9 + 8 + 5 + * + 8 + 6 + 5 = 9x
41 + * = 9x
Nearest value of 9x must be 45
41 + * = 45
* = 4```
 Question 4
The least perfect square, which is divisible by each of 15, 20 and 36 is:
 1200 800 1000 900

Question 4-Explanation:
```LCM of 15, 20 and 36 is 180

Now 180 = 3 x 3 x 2 x 2 x 5

To make it perfect square, it must
be multiplied from 5.

So required no. = 32 x 22 x 52 = 900```
 Question 5

Raghav has got a bag of numbers from 1 to 500, however he want to remove the numbers those are multiple of 9. How many total numbers will be removed?

 44 55 50 52

Question 5-Explanation:
```The required numbers are 9, 18, 27, 36, 45……450, 459, 468, 477, 486, 495

This is an A.P. with a = 9 and d = 9

Let it has n terms.

Then Tn = 495 = 9 + (n-1) x9

∴ 495 = 9 + 9n - 9

∴ 9n = 495

∴ n = 55```
 Question 6

Which digits should come in place of * and # if the number 4675*2# is divisible by both 5 & 8?

 4, 0 4, 5 1, 0 8, 0

Question 6-Explanation:

Since the given number is divisible by 5, 0 or 5 must come in place of \$. But a number ending with 5 is never divisible with 8 because a divisible number must be even. Therefore 0 will replace \$. If the number is divisible by 8, the number formed by last three digits must be divisible by 8. The number *20 must be divisible by 8. Among all 4 options, only placing 1 in place of * makes it divisible by 8.

 Question 7
What least number must be added to 4000 to obtain a number exactly divisible by 17?
 12 14 15 13

Question 7-Explanation:
```Let us divide 4000 by 17.

17) 4000 (235
34
….
60
51
…..
90
85
…..
5

We get 5 as remainder.
Number to be added = 17-5 = 12```
 Question 8

Gaurav is having 5000 chocolates and he decides to distribute these among his 23 friends. To make sure that every friend gets equal number of chocolates, he decides to eat x number of chocolates. What can be the minimum value of x?

 10 2 7 9

Question 8-Explanation:
```Let us divide 5000 by 23.

23) 5000 (217
46
….
40
23
….
170
161
…..
9

We get 9 as remainder.

Therefore required number to be subtracted = 9```
 Question 9

X is a positive 4 digit number. Find the largest possible value of X, such that on dividing with 5, 6, 7 it gives the remainder zero.

 9980 9870 9540 9640

Question 9-Explanation:
```The required number must be divisible by L.C.M. of 5,6 and 7.
L.C.M. of 5, 6 and 7 = 5 x 6 x 7 = 210

Let us divide 9999 by 210.

210) 9999 (47
840
----
1599
1470
----
129

Required number = 9999 – 129 = 9870```
 Question 10
34. What should be the next number in below series? 3, 8, 15, 24, 35……..
 44 47 48 49

Question 10-Explanation:
```Pattern is (22- 1), (32- – 1), (42- – 1), (52- – 1), ....

Next number will be = 72- – 1 = 49 – 1 = 48```
There are 16 questions to complete.