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a and b are integers such that a/b=3.45. If R is the remaind
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Updated on: 26 Apr 2014, 22:09
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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
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Originally posted by joyseychow on 21 Jan 2010, 01:06.
Last edited by Bunuel on 26 Apr 2014, 22:09, edited 2 times in total.
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Re: Remainder of a/b
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21 Jan 2010, 01:28




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Re: Remainder of a/b
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13 Feb 2010, 00:10
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/
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03 Dec 2010, 03:08
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/
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03 Dec 2010, 08:34
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/
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06 Dec 2010, 21:38
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 Raptor
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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 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? BTW the correct answer is (A)
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Originally posted by enigma123 on 28 Jun 2011, 21:25.
Last edited by Bunuel on 13 Jul 2013, 06:42, edited 1 time in total.
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Re: Decimals and Remainders
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28 Jun 2011, 22:17
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 HTH



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Re: Decimals and Remainders
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29 Jun 2011, 03:25
@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
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29 Jun 2011, 03:42
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 rewrite 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
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29 Jun 2011, 03:54
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
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29 Jun 2011, 10:11
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
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29 Jun 2011, 14:16
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
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01 Sep 2011, 20:35
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
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Re: a and b are integers such that a/b=3.45. If R is the remaind
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Re: a and b are integers such that a/b=3.45. If R is the remaind &nbs
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