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a and b are integers such that a/b=3.45. If R is the remaind

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a and b are integers such that a/b=3.45. If R is the remaind  [#permalink]

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New post Updated on: 26 Apr 2014, 23:09
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a and b are integers such that a/b=3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

A. 3
B. 9
C. 36
D. 81
E. 144

Originally posted by joyseychow on 21 Jan 2010, 02:06.
Last edited by Bunuel on 26 Apr 2014, 23:09, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Remainder of a/b  [#permalink]

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New post 21 Jan 2010, 02:28
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joyseychow wrote:
a and b are integers such that a/b=3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

A) 3
B) 9
C) 36
D) 81
E) 144


[spoiler]I've worked out R to be 9. Then I'm lost!! OA is B[/spoiler]


\(3.45=\frac{69}{20}\), which means that the ratio \(\frac{a}{b}=\frac{69}{20}\). \(a\) will be the multiple of \(69\) (\(a=69k\)) and \(b\) will be the multiple of \(20\) (\(b=20k\)). For ANY such \(a\) and \(b\), the remainder will be multiple of \(9\) --> \(a=qb+r\) --> \(69k=3*20k+9k\).

Only answer choice which is not the multiple of 9 is A (3).

Answer: A (3).
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Re: Remainder of a/b  [#permalink]

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New post 13 Feb 2010, 01:10
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joyseychow wrote:
a and b are integers such that a/b=3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

A) 3
B) 9
C) 36
D) 81
E) 144


[spoiler]I've worked out R to be 9. Then I'm lost!! OA is B[/spoiler]


3.45 = 3(9/20)

Now R can be a 9 or multiple of 9.
A is the figure less than 9 so answer is A
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Re: a and b are integers such that a/b = 3,45. If R is the remainder of a/  [#permalink]

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New post 03 Dec 2010, 04:08
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whichscore wrote:
a and b are integers such that a/b = 3,45. If R is the remainder of a/b, which of the following could not be equal to R ?
A. 3
B. 9
C. 36
D. 81
E. 144


Hi! This question is a great test of the concept of remainders.

Since a/b = 3.45, we can say that a/b = 345/100. Since a and b must be integers, the smallest possible values will be:

345/100 = 69/20

Rewriting 69/20 with a quotient and a remainder we get 3rem9.

Now we don't know the exact values of a and b, but since we can reduce a/b to 3rem9, we know that the remainder must be a multiple of 9 (and could be any multiple of 9).

B, C, D and E are all multiples of 9: choose (A).

For practice on this concept, there's a 12th edition O.G. question that's very similar - unfortunately, I don't have my copy at home, so I can't cite the exact question number.
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Re: a and b are integers such that a/b = 3,45. If R is the remainder of a/  [#permalink]

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New post 03 Dec 2010, 09:34
Hello...

To build on skovinsky's post, something to remember when you see a remainder question:

\(\frac{a}{b}=c+\frac{R}{b}\)

Since \(\frac{a}{b}=3.14\)...
\(3.14=3+\frac{R}{b}\)
Simplify...
\(0.14=\frac{R}{b}\)
Simplify again...
\(\frac{R}{b}=\frac{9}{20}\)

The last statement tells us that the remainder, R, is a multiple of 9 and the divisor, b, is a multiple of 20. As per answer choices, only A is not a multiple of 3.

Hence A.

HTHs.
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Re: a and b are integers such that a/b = 3,45. If R is the remainder of a/  [#permalink]

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New post 06 Dec 2010, 22:38
b X 0.45 = R

=> (R/0.45) should be an integer

A. 3 --> Not an integer
B. 9 --> Integer
C. 36 --> Integer
D. 81 --> Integer
E. 144 --> Integer

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a and b are integers such that a/b=3.45. If R is the remaind  [#permalink]

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New post Updated on: 13 Jul 2013, 07:42
a and b are integers such that a/b=3.45. If R is the remainder of a/b which of the following could NOT be equal to R?

A. 3
B. 9
C. 36
D. 81
E. 144

Ans: a/b=3.45

So considering decimal part: 0.45 = 45/100 where 45 is Remainder and 100 is divisor.

So, R/b=45/100 => 9/20 [I am fine until here]

How can I solve this question after here? Can someone please help? :cry:

BTW the correct answer is (A)
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Originally posted by enigma123 on 28 Jun 2011, 22:25.
Last edited by Bunuel on 13 Jul 2013, 07:42, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Decimals and Remainders  [#permalink]

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New post 28 Jun 2011, 23:17
R/b=45/100 => 9/20
therefore we have 20R = 9b
For the above to be true R must have a factor 9 as 20 doesnot have a factor 9
Now analyze the answer choices
All options except A have 9 as a factor hence R cannot be equal to A
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Re: Decimals and Remainders  [#permalink]

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New post 29 Jun 2011, 04:25
@toughmat,
I could not follow the course of the solution.
Why do we have to take R/b?
What does it denote?
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Re: Decimals and Remainders  [#permalink]

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New post 29 Jun 2011, 04:42
Because in the question stem it says a/b= 3.45 where a=Dividend and b=divisor. And when we have a remainder with a decimal as we have in this question (0.45) we can re-write this as 45/100 where 45 is the remainder. What we have done is put r=45. Does that make sense? If not then please let me know and I will elaborate.
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Re: Decimals and Remainders  [#permalink]

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New post 29 Jun 2011, 04:54
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enigma123 wrote:
a and b are integers such that a/b=3.45. If R is the remainder of a/b which of the following could NOT be equal to R?

a) 3
b) 9
c) 36
d) 81
e) 144


\(\frac{Dividend}{Divisor}=Quotient+\frac{Remainder}{Divisor}\)

\(\frac{a}{b}=Quotient+\frac{R}{b}\)--------------------1

3.45 can be written as:
\(3+0.45=3+\frac{45}{100}=3+\frac{9}{20}\) -----------------2

Correlate 1 and 2:
\(Quotient=3\)
\(\frac{R}{b}=\frac{9}{20}\)

\(20R=9b\) -----------------3

Expression 3 can only be true if "b" is a multiple of 20 AND "R" is a multiple of 9.

Out of all the options given, only "3" is NOT a multiple of 9.

Ans: "A"
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Re: Decimals and Remainders  [#permalink]

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New post 29 Jun 2011, 11:11
With a simple example -
5/2 = 2.5 = 2 + .5
=> 5 = 2.2 + 2*0.5.

Put the same thing here,
a = 3b + 0.45b

R = 0.45b, check from the options that which one is not divisible by .45. Only A.
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Re: Decimals and Remainders  [#permalink]

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New post 29 Jun 2011, 15:16
remainder = 9b/20

and b has to be an integer.

comparing 9b/20 with answer choices , we know Answer A gives non integer value for b.

Hence the answer is A.
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Re: Decimals and Remainders  [#permalink]

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New post 01 Sep 2011, 21:35
I agree with A.
Remainder = 0.45
= 45/100
= 9/20

Given, a/b = 3 + 9/29
Remainder(R) = 9b/20

and b has to be an integer.
comparing 9b/20 with answer choices , we know Answer A gives non integer value for b.

Hence the answer is A.
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Re: a and b are integers such that a/b=3.45. If R is the remaind  [#permalink]

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New post 21 Mar 2016, 09:40
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Re: a and b are integers such that a/b=3.45. If R is the remaind  [#permalink]

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New post 02 Jul 2019, 18:54
1
joyseychow wrote:
a and b are integers such that a/b=3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

A. 3
B. 9
C. 36
D. 81
E. 144



We can create the equation:

a/b = 3 + 45/100

a/b = 3 + 9/20

We see that the remainder is a multiple of 9, so 3 cannot be R.

Answer: A
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Re: a and b are integers such that a/b=3.45. If R is the remaind   [#permalink] 02 Jul 2019, 18:54
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