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# When positive integer a is divided by positive integer b, yielding quo

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Math Expert
Joined: 02 Sep 2009
Posts: 52344
When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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09 Oct 2016, 02:01
2
14
00:00

Difficulty:

75% (hard)

Question Stats:

56% (01:55) correct 44% (01:57) wrong based on 316 sessions

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When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?

A. r=1
B. q>r
C. b=8
D. 8r=b
E. 8b=r

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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09 Oct 2016, 04:18
6
5
Bunuel wrote:
When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?

A. r=1
B. q>r
C. b=8
D. 8r=b
E. 8b=r

Given is a=5.125b=(5+0.125)b...
Here 0.125b is the remainder...
So 0.125b=r...
0.125 is nothing but $$\frac{1}{8}$$......
So $$\frac{b}{8}=r........b=8r$$...
D
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##### General Discussion
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Joined: 04 Aug 2016
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Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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09 Oct 2016, 04:30
a/b = Q + r/b

r/b = 0.125 = 1/8

b=8r

D
Intern
Joined: 07 Nov 2015
Posts: 1
Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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08 Jun 2018, 01:02
What if we pick numbers 82 for a and 16 for b? Then D isn't true (r = 0.125, b = 16), but the intent of the passage is preserved, right?
Manager
Joined: 08 Sep 2016
Posts: 115
Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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08 Jun 2018, 16:51
a/b = q + r
a/b = 5 + .125

r/b = 125/1000

r/b = 1/8

8r=b
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Joined: 26 Mar 2013
Posts: 2001
Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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08 Jun 2018, 17:37
1
sakeofall wrote:
What if we pick numbers 82 for a and 16 for b? Then D isn't true (r = 0.125, b = 16), but the intent of the passage is preserved, right?

$$\frac{82}{16} = 5 + \frac{2}{16}$$

r/b = 2/16 = 1/8 = 0.125.........D holds true in that case too. b = 8r (16 = 8 *2)
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Re: When positive integer a is divided by positive integer b, yielding quo  [#permalink]

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12 Jun 2018, 10:09
1
Bunuel wrote:
When positive integer a is divided by positive integer b, yielding quotient q and remainder r, the result is 5.125. Which of the following must be true?

A. r=1
B. q>r
C. b=8
D. 8r=b
E. 8b=r

We can create the equations:

a/b = q + r/b

and

a/b = 5 + 0.125

a/b = 5 + 125/1000

a/b = 5 + 1/8

Thus,

r/b = 1/8

8r = b

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Re: When positive integer a is divided by positive integer b, yielding quo &nbs [#permalink] 12 Jun 2018, 10:09
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