In this type of questions there are basically four type of questions that can can be asked take a look.

**Type 1 :** These questions are very simple. We have to find value any one divisor, divident, quotient and remainder in which three values should be given or there may be a relation between them.

We can solve these type of questions just by putting values in following formula

Divident = Divisor × quotient + Remainder

**Type 2 :** When we have to find a smallest number that subtract from Divident to completely divisible.

In this case we divide number and remainder will be smallest number to subtract.

smallest number to subtract = remainder

**Type 3 :** When we have to find a smallest number that added to Divident to completely divisible.

In this case we will first find remainder then subtract remainder from Divisor then this number is the smallest number to ad.

smallest number to add = Divisor - remainder

**Type 4 :** on dividing a number with divisor-1 we have remainder-1. we have to find remainder when same number is divided by divisor-2.

First we check if divisor-1 is divisible by divisor-2 then remainder-2 will be remainder on dividing remainder-1 with divisor-2.

remainder-2 = (remainder-1) ÷ divisor-2

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Questions for practice

**Q1. **Smallest number that can be added to the greatest number of four digit so that the total sum is divided by 345

**a.** 50 **b.** 6 **c.** 60 **d.** 5

**Q2. **In a question of division divisor is 12 times of quotient and 5 times of remainder. if remainder is 36 then divident is

**a.** 2706 **b.** 2796 **c.** 2736 **d.** 2826

**Q3. **by which number 3274 is divided so that we get 96 quotient and 10 as a remainder

**a.** 34 **b.** 44 **c.** 54 **d.** 32

**Q4.** smallest number subtracted from 1155 so that the sum is completely divided by 14 is

**a.** 5 **b.** 9 **c.** 11 **d.** 7

**Q5. ** smallest number added to 3785 so that the sum is completely divided by 34 is

**a.** 11 **b.** 23 **c.** 9 **d.** 31

**Q6. **If a number is divided by 49 we get 32 as a remainder. if same number is divided by 7 then remainder is

**a.** 4 **b.** 3 **c.** 2 **d.** 5

**Q7. **If a number is divided by 280 we get 115 as a remainder. if same number is divided by 35 then remainder is

**a.** 15 **b.** 10 **c.** 20 **d.** 17

**Q8. **When x is divided by 289 we get 18 as a remainder. if x is divided by 17 then remainder is y. then y is -

**a.** 5 **b.** 2 **c.** 3 **d.** 1

**Q9.** When a number is divided by 56 we get 29 as a remainder. if same number is divided by 8 then remainder is

**a.** 6 **b.** 7 **c.** 4 **d.** 5

**Q10.** When a number is divided by 425 we get 45 as a remainder. if same number is divided by 17 then remainder is

**a.** 10 **b.** 11 **c.** 8 **d.** 9

**Answer Key**

**1. **b **2. **c **3. **a **4. **d **5. **b

**6. **a **7. **b **8. **d** ** **9. **d **10.** b