Remainders in Patterns

When a number is divided by 2, odd numbers always leave a remainder of 1, while even numbers leave a remainder of 0. Therefore, the correct choice is 'Odd numbers'.

When we divide 12 by 5, the quotient is 2 and the remainder is 2. Therefore, 12 is the correct answer as it leaves a remainder of 2 when divided by 5. Other options do not satisfy this condition.

A number has a remainder of 0 when divided by 8 if it is a multiple of 8. In this case, 24 is divisible by 8 (24 ÷ 8 = 3) with no remainder, while the other options (14, 18, and 30) are not multiples of 8.

To find the remainder when 47 is divided by 6, perform the division: 47 ÷ 6 = 7 with a remainder of 5. Therefore, the correct answer is B (5).

When 25 is divided by 7, it results in 3 with a remainder of 4 (as 25 = 7*3 + 4). Therefore, 25 is the correct answer because it satisfies the condition of giving a remainder of 4.

When we divide 19 by 9, the quotient is 2 and the remainder is 1. In contrast, 17 divided by 9 gives a remainder of 8, 27 divides evenly with a remainder of 0, and 36 also divides evenly with a remainder of 0.

When dividing 65 by 8, the quotient is 8 and the remainder is 1, since 8 times 8 equals 64, and 65 minus 64 gives a remainder of 1.

When a number is divided by 10, the remainder is the last digit of that number. In the case of 13, when divided by 10, the last digit is 3, which is the remainder. Therefore, 13 is the correct answer.

To determine which number gives a remainder of 2 when divided by 6, we can perform the division for each option. When we divide 14 by 6, the quotient is 2 and the remainder is 2. For 18, the remainder is 0; for 24, the remainder is also 0; and for 30, the remainder is 0 as well. Therefore, 14 is the only number that meets the condition.

When dividing 75 by 7, the quotient is 10 and the product of 10 and 7 is 70. The remainder is the difference between 75 and 70, which is 5. Therefore, the correct answer is B.

When a number leaves a remainder of 2 when divided by 9, it can be expressed in the form of 9k + 2, where k is an integer. Among the options, 20 is the only number that fits this form (9*2 + 2 = 20), while the others either leave different remainders or do not fit the equation.

A number leaves a remainder of 0 when it is divisible by another number without any leftover. In this case, 25 is divisible by 5 (25 ÷ 5 = 5) with no remainder, whereas 22, 26, and 27 leave remainders of 2, 1, and 2, respectively, when divided by 5.

To find which number gives a remainder of 3 when divided by 8, we can check each option. For 19, when divided by 8, the quotient is 2 and the remainder is 3 (19 = 8*2 + 3), satisfying the condition. The other options (15, 23, and 28) give remainders of 7, 7, and 4 respectively when divided by 8.

When dividing 92 by 9, we find how many times 9 fits into 92 completely. 9 fits into 92 ten times (since 9 x 10 = 90), leaving a remainder of 2 (92 - 90 = 2). Therefore, the remainder is 2.

When a number leaves a remainder of 1 when divided by 4, it can be expressed in the form 4k + 1, where k is an integer. The number 21 fits this criterion because when you divide 21 by 4, the quotient is 5 and the remainder is 1, thus confirming that 21 is the correct answer.

When dividing a number by 6, the remainder is what is left over after dividing. For example, 16 divided by 6 is 2 with a remainder of 4 (since 6 times 2 is 12, and 16 minus 12 equals 4). Thus, 16 is the correct answer as it leaves a remainder of 4 when divided by 6.

To determine which number leaves a remainder of 2 when divided by 7, we can check each option. Dividing each option by 7: 14 divided by 7 leaves a remainder of 0, 21 divided by 7 leaves a remainder of 0, 23 divided by 7 leaves a remainder of 2, and 28 divided by 7 leaves a remainder of 0. Therefore, the correct answer is 23 (option C).

When we divide 23 by 9, it gives us a quotient of 2 and a remainder of 5. This is because 23 can be expressed as 9 * 2 + 5, confirming that 23 is the correct answer.

A number is divisible by 12 if it can be divided by 12 without leaving a remainder. In this case, 36 is the only number among the options that meets this criterion, as 36 divided by 12 equals 3, which is an integer. The other options (22, 38, and 40) do not divide evenly by 12.

When dividing a number by 10, the remainder is the last digit of that number. The number 31 has a last digit of 1, so it leaves a remainder of 1 when divided by 10. The other options (35, 40, and 45) leave remainders of 5, 0, and 5 respectively.