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When 10 is divided by the positive integer n, the remainder
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09 Apr 2020, 01:45
09 Apr 2020, 01:45
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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
Kudos for the right answer and explanation
(A) 3
(B) 4
(C) 7
(D) 8
(E) 12
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
When 10 is divided by the positive integer n, the remainder
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09 Apr 2020, 06:03
09 Apr 2020, 06:03
1
Carcass wrote:
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
Kudos for the right answer and explanation
(A) 3
(B) 4
(C) 7
(D) 8
(E) 12
Kudos for the right answer and explanation
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
-------------------------
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
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When 10 is divided by the positive integer n, the remainder
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04 Sep 2022, 09:20
04 Sep 2022, 09:20
1
Given that when 10 is divided by the positive integer n, the remainder is n - 4 and we need to find which of the following could be the value of n
Theory: Dividend = Divisor*Quotient + Remainder
Lets solve the problem using two methods
Method 1: Substitution
Let's take each option choice and see which one satisfies the question
(A) 3
=> n = 3. But remainder cannot be 3-4 = -1 => NOT POSSIBLE
(B) 4
=> 10 when divided by 4 gives 2 remainder ≠ (4-4 =0) => NOT POSSIBLE
(C) 7
=> 10 when divided by 7 gives 3 remainder = (7-4 =3) => POSSIBLE
In Test, we don't need to solve further, but I am solving to complete the solution
(D) 8
=> 10 when divided by 8 gives 2 remainder ≠ (8-4 =4) => NOT POSSIBLE
(E) 12
=> 10 when divided by 12 gives 10 remainder ≠ (12-4 =8) => NOT POSSIBLE
So, Answer will be C
Method 2: Algebra
10 when divided by n gives n - 4 as remainder
10 -> Dividend
n -> Divisor
a -> Quotient (Assume)
n-4 -> Remainders
=> 10 = n*a + n-4 = na + n - 4
Putting a =1 we get
10 = n*1 + n - 4
=> 10 = n + n - 4 = 2n - 4
=> 2n = 10 + 4 = 14
=> n = \(\frac{14}{2}\) = 7
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
Lets solve the problem using two methods
Method 1: Substitution
Let's take each option choice and see which one satisfies the question
(A) 3
=> n = 3. But remainder cannot be 3-4 = -1 => NOT POSSIBLE
(B) 4
=> 10 when divided by 4 gives 2 remainder ≠ (4-4 =0) => NOT POSSIBLE
(C) 7
=> 10 when divided by 7 gives 3 remainder = (7-4 =3) => POSSIBLE
In Test, we don't need to solve further, but I am solving to complete the solution
(D) 8
=> 10 when divided by 8 gives 2 remainder ≠ (8-4 =4) => NOT POSSIBLE
(E) 12
=> 10 when divided by 12 gives 10 remainder ≠ (12-4 =8) => NOT POSSIBLE
So, Answer will be C
Method 2: Algebra
10 when divided by n gives n - 4 as remainder
10 -> Dividend
n -> Divisor
a -> Quotient (Assume)
n-4 -> Remainders
=> 10 = n*a + n-4 = na + n - 4
Putting a =1 we get
10 = n*1 + n - 4
=> 10 = n + n - 4 = 2n - 4
=> 2n = 10 + 4 = 14
=> n = \(\frac{14}{2}\) = 7
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
