Math Problems Quiz

The smallest positive number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is:

• 307

• 132

• 306

• 176

Answer explanation

The greatest 4-digit number is 9999. To find the smallest number to add for divisibility by 307, calculate 9999 mod 307, which gives a remainder of 132. Thus, adding 132 makes the sum divisible by 307.

How many numbers from 3 to 60 are odd numbers that are exactly divisible by 5?

• 7

• 5

• 8

• 6

Answer explanation

To find odd numbers between 3 and 60 that are divisible by 5, we list them: 5, 15, 25, 35, 45, 55. There are 6 such numbers, making the correct answer 6.

How many numbers between 300 and 1000 are divisible by 7?

• 994

• 301

• 101

• 100

Answer explanation

To find numbers between 300 and 1000 divisible by 7, calculate the first (301) and last (994) multiples of 7 in this range. The count is (994 - 301) / 7 + 1 = 100. Thus, the correct answer is 100.

Find the greatest number of five digits, which is exactly divisible by 468.

• 99684

• 99486

• 99864

• 99468

Answer explanation

To find the greatest five-digit number divisible by 468, divide 99999 by 468, which gives approximately 213. The product 213 * 468 = 99684, making it the largest five-digit number divisible by 468.

In between 250–1000, how many numbers are completely divisible by 5, 6 & 7.

• 5

• 7

• 6

• 3

Answer explanation

To find numbers divisible by 5, 6, and 7, calculate the LCM, which is 210. The multiples of 210 between 250 and 1000 are 420, 630, and 840. Thus, there are 3 such numbers.

The largest four-digit number that is exactly divisible by 83 is:

• 9936

• 9954

• 9960

• 9966

Answer explanation

To find the largest four-digit number divisible by 83, divide 9999 by 83, which gives approximately 120. Then, multiply 120 by 83 to get 9960, confirming it's the largest four-digit number divisible by 83.

A number when divided by 280 leaves 73 as the remainder. When the same number is divided by 35, the remainder will be:

• 4

• 2

• 3

• 7

Answer explanation

Let the number be x. We have x = 280k + 73 for some integer k. When divided by 35, 73 mod 35 = 3. Thus, the remainder when x is divided by 35 is 3.

The least number that is divisible by all the numbers from 2 to 10 is–

• 2520

• 100

• 504

• 9

Answer explanation

The least number divisible by all numbers from 2 to 10 is the least common multiple (LCM). The LCM of these numbers is 2520, as it is the smallest number that can be evenly divided by each of them.

How many numbers greater than 2 and less than 30 are divisible by 1 and themselves?

• 9

• 29

• 27

• 11

Answer explanation

The numbers greater than 2 and less than 30 that are divisible by 1 and themselves are the prime numbers: 3, 5, 7, 11, 13, 17, 19, 23, and 29. There are 9 such numbers.

371+372+373+374+375 is divisible by:

• 8

• 5

• 11

• 7

Answer explanation

The sum 371+372+373+374+375 equals 1865. Dividing 1865 by 11 gives a whole number (169), confirming that 1865 is divisible by 11. Thus, the correct answer is 11.