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Joined: 02 Sep 2009
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Math Expert
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Re M2839
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16 Sep 2014, 01:31
Official Solution: If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(x =divisor*quotient+remainder= yq + r\) and \(0 \leq r \lt y\). (1) \(y\) is a twodigit prime number. Clearly insufficient since we know nothinf about \(x\). (2) \(x=qy+9\), for some positive integer \(q\). It's tempting to say that this statement is sufficient and \(r=9\), since given equation is very similar to \(x =divisor*quotient+remainder= yq + r\) . But we don't know whether \(y \gt 9\)?: remainder must be less than divisor. For example: If \(x=10\) and \(y=1\) then \(10=1*1+9\), then the remainder upon division 10 by 1 is zero. If \(x=11\) and \(y=2\) then \(11=1*2+9\), then the remainder upon division 11 by 2 is one. Not sufficient. (1)+(2) From (2) we have that \(x=qy+9\) and from (1) that \(y\) is more than 9 (since it's a twodigit number), so we have direct formula of remainder, as given above. Sufficient. Answer: C
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Re: M2839
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16 Sep 2014, 22:23
Shouldn't x and y be interchanged in the answer explanation  considering question asks when x is divided by y, i.e. x is dividend and y is divisor?



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Re: M2839
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19 Sep 2014, 02:10



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Re: M2839
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28 Dec 2015, 09:11
Yes. I'll edit it to avoid confusion.[/quote]
This is still incorrect. X and Y have not been switched.



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Re: M2839
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18 Jan 2016, 19:36
msalvi wrote: Yes. I'll edit it to avoid confusion. This is still incorrect. X and Y have not been switched.[/quote] yup, very confusing  still not changed. thanks.
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Re: M2839
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21 Jan 2016, 11:13
I think this is a highquality question and I agree with explanation.



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Re: M2839
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02 Jan 2017, 06:00
Hi All, I don't understand the explanation.Taking statement 1 and 2 together and setting q to 1 we get x=y+9, which gives multiple remainders. Please advise, thanks.



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02 Jan 2017, 06:07



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Re: M2839
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05 Jan 2017, 11:25
Good Question



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Re: M2839
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07 Apr 2017, 21:50
Shouldn't x and y be interchanged in the answer explanation  Image considering question asks when x is divided by y, i.e. x is dividend and y is divisor?



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08 Apr 2017, 04:25



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Re M2839
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13 Jul 2017, 05:08
I think this is a poorquality question and I don't agree with the explanation. When you say "We don't know whether y>9?" Could you please elaborate. I have never seen that when divisor is 2 and dividend=11, the quotient can be 1. The definition of a remainder as stated is r<y.



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Re: M2839
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13 Jul 2017, 05:37
vil1 wrote: I think this is a poorquality question and I don't agree with the explanation. When you say "We don't know whether y>9?" Could you please elaborate. I have never seen that when divisor is 2 and dividend=11, the quotient can be 1. The definition of a remainder as stated is r<y. In (2) we are simply given that \(x=qy+9\). We are not given that when "x is divided by y the remainder is 9", we are just given that \(x=qy+9\). x, q, and y can be any set of positive integers satisfying this equation. Next, consider the examples given in the solution: If \(x=10\) and \(y=1\) then \(10=1*1+9\). In this case the remainder upon division x = 10 by y = 1 is zero. If \(x=11\) and \(y=2\) then \(11=1*2+9\). In this case then the remainder upon division x = 11 by y = 2 is one. Two different answers. Not sufficient.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: M2839
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08 Oct 2017, 05:02
This is a high quality question.
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