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When positive integer N is divided by positive integer J, the remainde

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When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 27 Feb 2015, 04:57
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When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22
B. 56
C. 78
D. 112
E. 175


Kudos for a correct solution.

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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 02 Mar 2015, 04:59
1
4
Bunuel wrote:
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22
B. 56
C. 78
D. 112
E. 175


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We know that \(decimal \ part \ of \ decimal \ quotient =\frac{remainder}{divisor}\)

So 0.08, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.
0.08 = 14/J
0.08*J = 14
J = 14/0.08 = 1400/8 = 700/4 = 350/2 = 175

So J = 175, answer = E.
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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 27 Feb 2015, 06:25
if we subtract remainder then there will be no decimal points

we have 0.08*x=14
x=175
n

Another example we have 2.4>>12/5 >>>>2 2/5>>> 2 is reminder so if we subtract 2 we get no remainder
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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 28 Feb 2015, 02:14
3
Bunuel wrote:
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22
B. 56
C. 78
D. 112
E. 175


Kudos for a correct solution.


When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 14
So, 134.08 = 134 + 14/J
So, J = 175

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When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 28 Sep 2018, 10:04
1
Bunuel wrote:
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22
B. 56
C. 78
D. 112
E. 175


Kudos for a correct solution.


comparing possible fractional values of .08 and answer choices,
note 2/25 and 175, a multiple of 25
confirming,
2/25*175=14 remainder
175
E
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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 18 Oct 2018, 18:55
Hi All,

To start, this question is a 'lift' of an Official Guide question:
OG2018 and OG2019 pg. 170, question #154

We're told that P and J are positive INTEGERS, when P is divided by J, the REMAINDER is 14 and N/J = 134.08. We're asked for the value of J. This question has a great 'math shortcut' built into it that can help you to avoid a calculation-heavy approach, but you have to pay careful attention to the answer choices.

Since N and J are INTEGERS and N/J = 134.08, we know that N = 134.08(J). Thus, whatever J is, when we multiply that number by 134.08 we end up with an INTEGER. This means that J has to 'cancel out' the decimal point. Put differently, the units digit of J multiplied by 8 has to create a number that ENDS in a 0. Looking at the 5 answer choices, there's only one answer that would do that...

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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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New post 19 Oct 2018, 06:08
Bunuel wrote:
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22
B. 56
C. 78
D. 112
E. 175

\(N,J \ge 1\,\,\,{\rm{ints}}\)

Let´s consider what the Division Algorithm say!

\(N = QJ + 14\,\,,\,\,\,\left\{ \matrix{
\,Q\,\,{\mathop{\rm int}} \hfill \cr
\,J \ge 15\,\,\,\,\,,\,\,\,\,\,\,? = J\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left( * \right)\)

\(134.08 = {N \over J} = Q + {{14} \over J}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left\{ \matrix{
\,Q = 134 \hfill \cr
\,{{14} \over J} = 0.08 = {8 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = J = {{14 \cdot 100} \over 8} = 7 \cdot 25 = 175 \hfill \cr} \right.\,\,\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: When positive integer N is divided by positive integer J, the remainde &nbs [#permalink] 19 Oct 2018, 06:08
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