1.
If the sum of the digits of a number is divisible by 3, then the number will be divisible by which of the following?
Correct Answer
A. 3
Explanation
If the sum of the digits of a number is divisible by 3, then the number will be divisible by 3 as well. This is because when a number is divisible by 3, the sum of its digits is also divisible by 3. Therefore, if the sum of the digits of a number is divisible by 3, it implies that the number itself is divisible by 3.
2.
Which number is divisible by 2?
Correct Answer
B. 236
Explanation
The number 236 is divisible by 2 because it ends in an even digit, which means it is an even number. In contrast, the other numbers listed (123, 237, and 345) do not end in even digits and are therefore not divisible by 2.
3.
1000 can be divisible by which number here?
Correct Answer
D. 2 and 5 both
Explanation
1000 can be divided evenly by both 2 and 5. When a number is divisible by 2, it means that it can be divided into two equal parts without leaving any remainder. Similarly, when a number is divisible by 5, it means that it can be divided into five equal parts without leaving any remainder. In the case of 1000, it can be divided by 2 to give 500 and by 5 to give 200. Therefore, the correct answer is that 1000 is divisible by both 2 and 5.
4.
Which number is divisible by both 2 and 3?
Correct Answer
A. 126
Explanation
The number 126 is divisible by both 2 and 3 because it is an even number (divisible by 2) and the sum of its digits (1+2+6) is 9, which is divisible by 3. Therefore, 126 satisfies the conditions of being divisible by both 2 and 3.
5.
Which number is divisible by 9?
Correct Answer
D. 78534
Explanation
The number 78534 is divisible by 9 because the sum of its digits is divisible by 9. In this case, 7+8+5+3+4=27, which is divisible by 9. Therefore, 78534 is divisible by 9.
6.
Which number is divisible by both 3 and 9?
Correct Answer
B. 78534
Explanation
The number 78534 is divisible by both 3 and 9 because the sum of its digits (7+8+5+3+4) is equal to 27, which is divisible by both 3 and 9.
7.
15000 can be divisible by which number here?
Correct Answer
D. All of the above
Explanation
The number 15000 can be divided evenly by 2 because it is an even number. It can also be divided evenly by 3 because the sum of its digits (1+5+0+0+0) is divisible by 3. Additionally, it can be divided evenly by 5 because it ends in 0 or 5. Therefore, all of the given numbers (2, 3, and 5) can divide 15000 evenly.
8.
What numbers are divisible by 2, 3, and 10 at the same time?
Correct Answer(s)
B. 30
D. 120
Explanation
The numbers that are divisible by 2, 3, and 10 at the same time are called common multiples. In this case, 30 and 120 are the common multiples. Both 30 and 120 can be divided evenly by 2, 3, and 10, making them the correct answers.
9.
The number 203 is divisible by 3 and 7
Correct Answer
B. False
Explanation
The number 203 is not divisible by 3 because the sum of its digits (2+0+3) is not divisible by 3. Additionally, 203 is not divisible by 7 because it does not end in a 7 or a 0. Therefore, the statement is false.
10.
36 is divisible by
Correct Answer
C. 2
Explanation
The number 36 is divisible by 2 because it is an even number.