When a is divided by 7,the remainder is 4.When b is divided by 3,the remainder is 2.If 0<a<24 and 2<b<8, which of the following could have a remainder of 0 when divided by 8?

a. a/b
b. b/a
c. a-b
d. a+b
e. ab

please answer and explain

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To find which of the given expressions could have a remainder of 0 when divided by 8, we need to evaluate each expression and check if it is divisible by 8.

Given information:
- When a is divided by 7, the remainder is 4.
- When b is divided by 3, the remainder is 2.
- 0 < a < 24
- 2 < b < 8

a. a/b:
We know that when a is divided by 7, the remainder is 4. However, since the range of b is 2 < b < 8, and we need to divide a by b, there is no guarantee that a/b will result in a remainder of 0. Therefore, it is not a possible option.

b. b/a:
Similarly, since the range of a is 0 < a < 24, and we need to divide b by a, there is no guarantee that b/a will result in a remainder of 0. Therefore, it is not a possible option.

c. a-b:
Since a is divisible by 7 with a remainder of 4, and b is divisible by 3 with a remainder of 2, we can evaluate a-b. Let's assume a = 11 and b = 5:

a = 7 * 1 + 4
b = 3 * 1 + 2

a - b = (7 * 1 + 4) - (3 * 1 + 2) = 4 - 2 = 2

Since 2 is not divisible by 8, a-b cannot have a remainder of 0. Therefore, it is not a possible option.

d. a+b:
Using the same assumption of a = 11 and b = 5:

a + b = (7 * 1 + 4) + (3 * 1 + 2) = 11 + 5 = 16

Since 16 is divisible by 8, a+b can have a remainder of 0. Therefore, it is a possible option.

e. ab:
Using the same assumption of a = 11 and b = 5:

ab = (7 * 1 + 4) * (3 * 1 + 2) = 11 * 5 = 55

Since 55 is not divisible by 8, ab cannot have a remainder of 0. Therefore, it is not a possible option.

In conclusion, the expression that could have a remainder of 0 when divided by 8 is d. a+b.

To find out which of the given expressions could have a remainder of 0 when divided by 8, we need to analyze the possible values of a and b.

We are given that when a is divided by 7, the remainder is 4. It means a can have the following values that satisfy this condition:
a = 4, 11, 18

Similarly, when b is divided by 3, the remainder is 2. It means b can have the following values:
b = 2, 5

Now, let's analyze each expression:

a. a/b:
For a = 4 and b = 2, a/b = 4/2 = 2. Since 2 divided by 8 leaves a remainder of 2, option a is not divisible by 8 without a remainder.

b. b/a:
For a = 4 and b = 2, b/a = 2/4 = 0.5. Since 0.5 is not an integer, option b cannot have a remainder of 0 when divided by 8.

c. a-b:
For a = 4 and b = 2, a-b = 4-2 = 2. Since 2 divided by 8 leaves a remainder of 2, option c is not divisible by 8 without a remainder.

d. a+b:
For a = 4 and b = 2, a+b = 4+2 = 6. Since 6 divided by 8 leaves a remainder of 6, option d is not divisible by 8 without a remainder.

e. ab:
For a = 4 and b = 2, ab = 4*2 = 8. Since 8 divided by 8 leaves a remainder of 0, option e is divisible by 8 without a remainder.

Based on the analysis, the expression that could have a remainder of 0 when divided by 8 is option e: ab.

well, clearly,

a is 11 or 18
b is 5

Now pick the correct answer.