Remainders

cazubuine wrote:Would someone be willing to share with me how you solve this problem?

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when is divided by B?
(a)13 (b) 14 (c) 15 (d) 16 (e) 17

We're told that A/B = 4.35
In other words, A/B = 435/100
Simplify: A/B = 87/20
87 divided by 20 gives us a remainder of 7. Check the answer choices: 7 is not an option.

Aside: At this point, we may might recognize that if we double 87 and 20, the remainder will also be doubled, to get [spoiler]14 = B[/spoiler] Or, we can continue with our other line of thought . . .

Since 87 divided by 20 didn't yield a remainder found in the answer choices, let's try a fraction that's equivalent to 87/20
How about 174/40?
174 divided by 40 gives us a remainder of 14. Check the answer choices: 14 is an option.
Answer: B

Cheers,
Brent

cazubuine wrote:Would someone be willing to share with me how you solve this problem?

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when is divided by B?
(a)13 (b) 14 (c) 15 (d) 16 (e) 17

Another approach:

A/B = 4.35
Multiply both sides by B to get: A = 4.35B
Rewrite as A = (4 + 0.35)B
Expand: A = 4B + 0.35B

IMPORTANT: If we divide A by B, the remainder will be 0.35B
0.35B = (7/20)B = (7)(B/20)
This tells us two things:
1) B will be a multiple of 20 (in order for the remainder to be an integer).
2) Since the remainder = (7)(B/20), the remainder must be a multiple of 7.

Only answer choice B is a multiple of 7

Cheers,
Brent