When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Oct 08, 2020 4:07 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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Source: Beat The GMAT — Problem Solving | Thu Oct 08, 2020 4:07 pm

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

by swerve » Thu Oct 08, 2020 5:19 pm

BTGmoderatorDC wrote: ↑
Thu Oct 08, 2020 4:07 pm
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

Comparing possible fractional values of .08 and answer choices,
note $\dfrac{2}{25}$ and $175$, a multiple of $25$
confirming,
$\dfrac{2}{25} \cdot 175=14$ remainder

$175\Longrightarrow$E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

by Scott@TargetTestPrep » Mon Oct 12, 2020 4:11 am

BTGmoderatorDC wrote: ↑
Thu Oct 08, 2020 4:07 pm
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

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

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