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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
When positive integer N is divided by positive integer J, the remainde  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (01:39) correct 19% (02:02) wrong based on 160 sessions

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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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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Manager  Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 74
Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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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
SVP  B
Joined: 06 Nov 2014
Posts: 1877
Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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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

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course VP  P Joined: 07 Dec 2014 Posts: 1191 When positive integer N is divided by positive integer J, the remainde [#permalink] ### Show Tags 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 EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14188 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: When positive integer N is divided by positive integer J, the remainde [#permalink] ### Show Tags 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... Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
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Re: When positive integer N is divided by positive integer J, the remainde  [#permalink]

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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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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: When positive integer N is divided by positive integer J, the remainde   [#permalink] 19 Oct 2018, 07:08
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# When positive integer N is divided by positive integer J, the remainde

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