When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n.
A) 9
B) 20
C) 55
d) 70
e) 81
Tricky remainder problem
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- ceilidh.erickson
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If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k:
xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11
0.2n = 11
n = 55
The answer is C.
xn + 11 = k
If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.
k = 81.2n
and
k = 81n + 11
Now, we can simply set these expressions equal to each other, since they're both equal to k:
81.2n = 81n + 11
0.2n = 11
n = 55
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Hi mgm,
Ceilidh has shown an algebraic solution to this question. Here's a solution that's based more on Number Properties and a bit of "brute force" math.
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has to "multiply out" the .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
Ceilidh has shown an algebraic solution to this question. Here's a solution that's based more on Number Properties and a bit of "brute force" math.
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has to "multiply out" the .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.mgm wrote:When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n.
A) 9
B) 20
C) 55
d) 70
e) 81
There is a relationship between the two representations:
Remainder/Divisor = Decimal.
When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.
It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.
In the problem above:
Remainder = 11.
Divisor = n.
Decimal = .2 = 2/10 = 1/5.
Plugging these values into remainder/divisor = decimal, we get:
11/n = 1/5
n = 55.
The correct answer is C.
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Use a simpler technique
.2 x n = 11
n = 11/0.2 = 55
Answer [spoiler]{C}[/spoiler]
For example: 11/5 --> 2.2 so .2 * 5 = 1 (remainder)
.2 x n = 11
n = 11/0.2 = 55
Answer [spoiler]{C}[/spoiler]
For example: 11/5 --> 2.2 so .2 * 5 = 1 (remainder)
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When the positive integer k is divided by the positive integer n and the remainder is 11 we know that: k = x.n + 11 (equation 1), where x is the quotient and y is the remainder.
We also know that k/n = 81.2 or k = 81.2.n (equation 2)
From equation 2 we know that x = 81 (the quotient) --> k = 81.n + 11 (equation 3)
Using equations 2 and 3 --> 81.2n = 81.n + 11
0.2n = 11
n = 55
We also know that k/n = 81.2 or k = 81.2.n (equation 2)
From equation 2 we know that x = 81 (the quotient) --> k = 81.n + 11 (equation 3)
Using equations 2 and 3 --> 81.2n = 81.n + 11
0.2n = 11
n = 55
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How about something completely different? We know from the prompt that
k = n*(something) + 11
and
k = 81.2n
So we know that
n*(something) + 11 = 81.2n
Multiplying both sides by 5 then subtracting 5n*(something) from both sides, we get
55 = 406n - 5n*(something)
Since the left hand side is a multiple of 55, the right hand side must be a multiple of 55. This is only possible (at least with integers) if n is a multiple of 55, so C.
k = n*(something) + 11
and
k = 81.2n
So we know that
n*(something) + 11 = 81.2n
Multiplying both sides by 5 then subtracting 5n*(something) from both sides, we get
55 = 406n - 5n*(something)
Since the left hand side is a multiple of 55, the right hand side must be a multiple of 55. This is only possible (at least with integers) if n is a multiple of 55, so C.
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We can create two remainder equations:mgm wrote:When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n.
A) 9
B) 20
C) 55
d) 70
e) 81
k/n = 81 + 2/10
k/n = 81 + 1/5
and
k/n = 81 + 11/n
Thus:
1/5 = 11/n
n = 55
Answer: C
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