Successive Division

Q.

During a sale, color pencils were being sold in packs of $24$ each and crayons in packs of $32$ each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy?

Q.

The least number, which when divided by 48, 60, 72, 108 and 140 leaves remainders as 38, 50, 62, 98 and 130 respectively, is :

1. 15110

2. 11115

3. 15120

4. 15210

5. 15220

Q.

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

1. 9800

2. 9200

3. None of these

4. 9400

5. 9600

Q.

Three friends A, B and C start running around a circular stadium and complete a single round in 8, 18 and 15 seconds respectively. After how many minutes will they meet again at the starting point for the first time?

1. 12

2. 6

3. 8

4. 18

5. 15

Q.

Find the smallest number which on being added $23$ to it, is exactly divisible by $32,36,48,96.$

Q.

What is the smallest number which when increased by 5 is divisible by 36, 63 and 108?

1. 756

2. 751

3. 752

4. 753

5. 754

Q.

Find the greatest number of four digits which when divided by 10, 11, 15, and 22 leaves 3, 4, 8 and 15 as remainders respectively.

1. 9900

2. 9903

3. 8900

4. 9992

5. 9893

Q.

Two alarm clocks ring their alarms at regular intervals of 60 seconds and 90 seconds. If they first beep together at 12 noon, at what time will they beep again together for the first time?

1. 12:01 PM

2. 12:03 PM

3. 12:04 PM

4. 12:05 PM

Q. Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, and 16 is 4?

(CAT 1994)

1. 172
2. 137
3. 1361
4. 140

Q.

In first 1000 natural numbers, how many numbers exists such that when divided by 7 leaves a remainder of 6?

1. 141

2. 143

3. 146

4. 142

Q. Three friends J, K and L jog around a circular stadium and complete one round in 12, 18 and 20 seconds respectively. In how many minutes will all the three meet again at the starting point?

1. 5
2. 8
3. 12
4. 3
5. None of these

Q.

What will come in place of the question mark (?) in each of the following series?

124, 112, 176, 420, 1488, ?

1. None of these

2. 5712

3. 6150

4. 3568

5. 7140

Q.

The sum of first 19 multiples of 28 is

1. 5370

2. 5340

3. 5320

4. None of these

Q.

If $U=\left\{x:xisanaturalnumberlessthan20\right\}$, then find its subsets $R$ such that

$R=\left\{primenumbers\right\}$

Q. How many three digit numbers have a digital root = 5?

1. 10
2. 20
3. 100
4. 99

Q.

The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is :

1. 3

2. 13

3. 23

4. 33

5. 41

Q. Find the least number which when divided by $25,40$ and $60$ leaves $9$ as the remainder in each case.

Q.

Find the least number which when divided by 48, 60, 165 leaves a remainder of 19, 31 and 136 respectively in each case.

1. 5251

2. 10531

3. 13171

4. None of these

5. 7891

Q. How many three digit numbers have a digital root = 5?

1. 10
2. 100
3. 20
4. 80
5. 99

Q. Find the least number which when divided by 6, 7, 8, 9 and 10 leaves remainder 1

Q.

Two alarm clocks ring their alarms at regular intervals of 60 seconds and 90 seconds. If they first beep together at 12 noon, at what time will they beep again together for the first time?

1. 12:02 PM

2. 12:03 PM

3. 12:04 PM

4. 12:05 PM

5. 12:01 PM

Q.

Find the greatest number of four digits which when divided by 10, 11, 15, and 22 leaves 3, 4, 8 and 15 as remainders respectively.

1. 9900

2. 9893

3. 9903

4. 8900

Q.

The smallest four digit number which is divisible by $18,24and32,$is

1. $432$

2. $768$

3. $576$

4. $1152$

Q. The difference between two positive integers is $13$ and their product is $140$. Find the two integers.

1. $12$ and $13$
2. $7$ and $13$
3. $20$ and $3$
4. $7$ and $20$