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When positive integer N is divided by positive integer J,

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by BTGmoderatorDC » Thu Oct 18, 2018 6:16 pm
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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

OA E

Source: Magoosh
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by [email protected] » Thu Oct 18, 2018 6:24 pm
Hi All,

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

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by Byjus » Fri Oct 19, 2018 1:45 am
Hi,

Yes, this is a very popular question in GMAT.

Using simple logic we can solve this question in few seconds,

For example,

5 divided by 2, the remainder is 1 and but 5/2 = 2.5

One thing, we can notice above is we get 2.5 because 2 is the quotient and .5 is the value when the remainder is divided by 2.

i.e.,

5 = 2*2 + 1

We get decimal value(0.5) because remainder is divided by the divisor.

So Similarly here,

N/J = 134.08,

So here the decimal value 0.08 is because when remainder 14/ J = 0.08

14/ J = 0.08

14/ 0.08 = J

J = 1400/8

J = 175

So the answer is E.
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by GMATGuruNY » Fri Oct 19, 2018 3:53 am
BTGmoderatorDC 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 = 134.08 = 13408/100 = 3352/25.
The resulting ratio indicates that N must be multiple of 3352 and that J must be a multiple of 25.
Of the five answer choices, only E is a multiple of 25.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Oct 19, 2018 5:02 am
BTGmoderatorDC 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
ASIDE: 7/2 = 3 1/2 = 3 + 0.5 = 3.5 Notice that 1 is the remainder when we divide 7 by 2.
23/5 = 4 3/5 = 4 + 0.6 = 4.6 Notice that 3 is the remainder when we divide 23 by 5.
31/4 = 7 3/4 = 7 + 0.75 = 7.75 Notice that 3 is the remainder when we divide 31 by 4.

GIVEN: N/J = 134.08
This means 14/J = 0.08
So, J = 14/0.08 = 175

Answer: E

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by fskilnik@GMATH » Fri Oct 19, 2018 6:02 am
BTGmoderatorDC 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
Source: Magoosh
\[N,J \geqslant 1\,\,\,{\text{ints}}\]
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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