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.

Tick

165150

Cross

1600843

Cross

168132420

Cross

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 ?
Tick
546702
Cross
556824
Cross
367312
Cross
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?
Cross
6
Cross
5
Tick
4
Cross
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:
Cross
1200
Cross
800
Cross
1000
Tick
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?

Cross

44

Tick

55

Cross

50

Cross

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?

Cross

4, 0

Cross

4, 5

Tick

1, 0

Cross

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?
Tick
12
Cross
14
Cross
15
Cross
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?

Cross

10

Cross

2

Cross

7

Tick

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.

Cross

9980

Tick

9870

Cross

9540

Cross

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……..
Cross
44
Cross
47
Tick
48
Cross
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.


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