Vincen wrote: ↑Tue Jun 30, 2020 6:34 am
When 10 is divided by the positive integer \(n,\) the remainder is \(n - 4.\) Which of the following could be the value of \(n?\)
(A) 3
(B) 4
(C) 7
(D) 8
(E) 12
[spoiler]OA=C[/spoiler]
Source: Official Guide
APPROACH #1: I'd say that the fastest approach is to simply test answer choices
(A) 3
The question tells us that we get a remainder of n - 4
So, if n = 3, then the remainder = 3 - 4 = -1, which makes no sense (the remainder must always be greater than or equal to 0)
Eliminate A
(B) 4
Plug n = 4 into the given information to get: When 10 is divided by 4, the remainder is 4 - 4 (aka 0)
This is not true. When we divide 10 by 4, we get reminder 2
Eliminate B
(C) 7
Plug n = 7 into the given information to get: When 10 is divided by 7, the remainder is 7 - 4 (aka 3)
WORKS!
Answer: C
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APPROACH #2: Apply the rule for rebuilding the dividend
There's a nice rule that says, "
If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
Given: When 10 is divided by the positive integer n, the remainder is n - 4
Since we're not told what the quotient is, let's just say that it's q.
In other words: When 10 is divided by the positive integer n, the quotient is q, and the remainder remainder is n - 4
When we apply the above rule we get: 10 = nq + (n-4)
Add 4 to both sides of the equation to get: 14 = nq + n
Factor to get: 14 = n(q + 1)
Importance: Since n and (q + 1) are INTEGERS, n must be a FACTOR of 14.
Check the answer choices.... only answer choice C (7) is a factor of 14
Answer: C
Cheers,
Brent
