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

Question

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

Bunuel · Accepted Answer

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.

OptimusPrepJanielle · Answer

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: https://www.optimus-prep.com/gmat-on-demand-course

ynaikavde · Answer

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

gracie · Answer

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

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made, 
Rich

fskilnik · Answer

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.

ScottTargetTestPrep · Answer

Solution:
 
We can create the equation:

N/J = 134 + 8/100

N/J = 134 + 2/25

But we are also given that the remainder is 14. In other words, we have:

N/J = 134 + 14/J

Setting 2/25 = 14/J, we have:

2J = 14 x 25

2J = 350

J = 175

Answer: E

ravigupta2912 · Answer

If you try to reframe this, you'll get that 14 is equal to 8% (134.08) of something. We need to find that "something"

14 = 8/100*x
=> 1400/8 = x
=> 350 / 2 = x

I didn't even solve further. I knew that the next number had to end in 5 and that there was only 1 possible choice for it.

bumpbot · Answer

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

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