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# For positive integers a and b, when a is divided by b the remainder is

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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18 Apr 2017, 04:06
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:21) correct 24% (01:53) wrong based on 181 sessions

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For positive integers a and b, when a is divided by b the remainder is 12. If a/b = 32.16, what is the value of b?

A. 25
B. 32
C. 64
D. 75
E. 96

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Location: India
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Re: For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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18 Apr 2017, 05:49
Since a/b = 32.16, the quotient is 32
Remainder is .16*x = 12
x = 12/.16 = 1200/16 = 300/4 = 75(Option D)

To check if our answer is correct, 75*32 + 12 = 2412.
This when divided by 75 gives us 32.16
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Re: For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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18 Apr 2017, 14:37
Bunuel wrote:
For positive integers a and b, when a is divided by b the remainder is 12. If a/b = 32.16, what is the value of b?

A. 25
B. 32
C. 64
D. 75
E. 96

16/100=12/b
b=75
D
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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24 Apr 2017, 15:55
2
1
Bunuel wrote:
For positive integers a and b, when a is divided by b the remainder is 12. If a/b = 32.16, what is the value of b?

A. 25
B. 32
C. 64
D. 75
E. 96

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer a is divided by positive integer b, if integer Q is the quotient and r is the remainder, then a/b = Q + r/b.

In this problem, we are given that when positive integer a is divided by positive integer b, the remainder is 12. So, we can say:

a/b = Q + 12/b

We also are given that a/b = 32.16. Using the remainder formula, we can say:

a/b = 32.16

a/b = 32 + 0.16

a/b = 32 + 16/100

Because Q is always an integer, we see that Q must be 32, and thus the remainder 12/b must be 16/100. We can now equate 12/b to 16/100 and determine the value of b.

12/b = 16/100

12/b = 4/25

12 x 25 = 4b

3 x 25 = b

75 = b

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For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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24 Apr 2017, 17:12
I would do process elimination for this
a/b = 32.16
a/b = 32 4/25

Answer B, C and E are incorrect because they are not multiple of 25.

Then I would do process elimination further

A 25 x 32 = 800 + 12 (Remainder) = 812

812/25 = 32.48. Not the answer

D 75 x 32 = 2400 + 12 (Remainder) = 2412

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Joined: 11 Feb 2017
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Location: India
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Re: For positive integers a and b, when a is divided by b the remainder is  [#permalink]

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23 May 2017, 12:50
Since a/b = 32.16, Rem is 0.16*b = 12; b = 12/.16 = 1200/16 = 300/4 = 75(Option D)
Re: For positive integers a and b, when a is divided by b the remainder is &nbs [#permalink] 23 May 2017, 12:50
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