Tricky remainder problem

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mgm: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Sep 12, 2010 12:32 pmFollowed by: 1 member; Thanked: 1 times

by mgm » Tue Oct 01, 2013 1:33 pm

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

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Source: Beat The GMAT — Problem Solving | Tue Oct 01, 2013 1:33 pm

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Oct 01, 2013 2:18 pm

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.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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by [email protected] » Tue Oct 01, 2013 6:39 pm

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

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Rich

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 02, 2013 2:39 am

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

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
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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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Oct 02, 2013 3:09 am

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)

R A H U L

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pier.ferraro: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Sep 20, 2014 1:31 pm; Location: London, United Kingdom; GMAT Score:470

by pier.ferraro » Wed Dec 17, 2014 3:34 am

If K/N is 81,2 and the remainder is 11 we can say that 11=0,2n
11/0,2=55
N=55

Answer C

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mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 amFollowed by: 4 members; Location: London, UK; Thanked: 2 times; GMAT Score:770

by mbawisdom » Wed Dec 17, 2014 7:50 am

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

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Fri Dec 19, 2014 4:45 am

0.2 = 1/5, so n must be a multiple of 5 and/or a multiple of 11
Only 55 meets these criteria

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Dec 22, 2014 12:43 pm

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.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Jan 05, 2018 7:02 am

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

We can create two remainder equations:

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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Founder and CEO
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