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When positive integer x is divided by 5, the remainder is 2.
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Updated on: 15 Jun 2014, 04:40
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When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following cannot be the sum x + y? A. 12 B. 13 C. 14 D. 16 E. 21
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Originally posted by Critique on 15 Jun 2014, 04:20.
Last edited by Bunuel on 15 Jun 2014, 04:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




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Re: When positive integer x is divided by 5, the remainder is 2.
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15 Jun 2014, 04:41
Critique wrote: When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following cannot be the sum x + y?
A. 12 B. 13 C. 14 D. 16 E. 21 When positive integer x is divided by 5, the remainder is 2: x could be 2, 7, 12, 17, ... When positive integer y is divided by 4, the remainder is 1: y could be 1, 5, 9, 13, 17, ... If x is 7 and y is 5, then x + y = 12. Eliminate A. If x is 12 and y is 1, then x + y = 13. Eliminate B. If x is 7 and y is 9, then x + y = 16. Eliminate D. If x is 12 and y is 9, then x + y = 21. Eliminate E. By process of elimination the correct answer must be C. Answer: C P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to rules 3 and 7. Thank you.
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Re: When positive integer x is divided by 5, the remainder is 2.
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16 Jun 2014, 23:13
Answer = C = 14 Please refer screenshot below for possible combinations
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Re: When positive integer x is divided by 5, the remainder is 2.
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20 Jun 2016, 20:54
One way to solve this problem: since x=5a+2, where a is an integer. and y=4b+1 where b is an integer x+y=5a+4b+3..
now test for integer solutions of a and b. We need to subtract 3 from answer choice and then test whether the resultant can be expressed 5a+4b. choice a) 12. Subtract 3 we get 9 . 9 = 4a+5b. take a=1, b=1. choice b) 13. Subtract 3 we get 10. 10=4a+5b. take a=0 and b=2. choice c) 14. Subtract 3 we get 11. 11 = 4a+5b. if we take a=0, 1,2, can we have b which is positive integer. let us check a=0 ;11=5b , a = 1 ; 7 = 5b, a = 2 ; 3= 5b, a = 3 , now in this case 1 = 5b.. now from here on we can get negative values on the L.H.S. So we cannot express 11 = 4a+5b where a and b are integers. This is our answer. choice d) 16 . Subtract 3 we get 13 . 13= 4a+5b. take a =2 and b = 1. choice e) 21. subtract 3 we get 18. 18= 4a+5b. take a=2, b=2. Done!



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Re: When positive integer x is divided by 5, the remainder is 2.
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09 Nov 2016, 15:23
y=5r+2 (2,7,12,17,....)
x=4r+1 (1,5,9,13,....)
C is the only number you cannot create using any combination of x and y



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Re: When positive integer x is divided by 5, the remainder is 2.
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06 Sep 2017, 09:13
Bunuel how do you know the possible values of X? How does 2/5 give a remainder of 2?



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Re: When positive integer x is divided by 5, the remainder is 2.
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06 Sep 2017, 09:23
bkastan wrote: Bunuel how do you know the possible values of X? How does 2/5 give a remainder of 2? 1. If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).So, positive integer x is divided by 5, the remainder is 2 means that x = 5q + 2, thus x could be 2, 7, 12, ... 2. Let me ask you a question: how many leftover apples would you have if you had 2 apples and wanted to distribute in 5 baskets evenly? Each basket would get 0 apples and 2 apples would be leftover (remainder). When a divisor is more than dividend, then the remainder equals to the dividend, for example: 3 divided by 4 yields the reminder of 3: \(3=4*0+3\); 9 divided by 14 yields the reminder of 9: \(9=14*0+9\); 1 divided by 9 yields the reminder of 1: \(1=9*0+1\). For more on this check: 5. Divisibility/Multiples/Factors 6. Remainders For other subjects: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative Megathread
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Re: When positive integer x is divided by 5, the remainder is 2.
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06 Sep 2017, 09:40
Bunuel thank you!!! Posted from my mobile device



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Re: When positive integer x is divided by 5, the remainder is 2.
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06 Sep 2017, 22:31
Critique wrote: When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following cannot be the sum x + y?
A. 12 B. 13 C. 14 D. 16 E. 21 x=5q+2 y=4p+1 x+y=5q+4p+3 12: q=1;p=1 13: q=2;p=0 16: q=1;p=2 21: q=2;p=2 14: no C



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Re: When positive integer x is divided by 5, the remainder is 2.
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07 Sep 2017, 03:40
Note that 1 + 2 = 3. Deduct 3 from every proposed answer and try to construct the resulting figure with 5s and 4s.
A. 12 3 = 9 = 5+4 B. 13 3 =10= 5+ 5 C. 14 3 = 11= correct answer D. 16 3 = 13 = 5+4+4 E. 21 3 = 18= 4+4 +5+5



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Re: When positive integer x is divided by 5, the remainder is 2.
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11 Sep 2017, 11:35
Critique wrote: When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following cannot be the sum x + y?
A. 12 B. 13 C. 14 D. 16 E. 21 We can create the following equations: x = 5Q + 2 Some values for x are 2, 7, 12, 17. y = 4Z + 1 Some values for y are 1, 5, 9, 13, 17. Let’s go through each answer choice: A) 12 Since 7 + 5 = 12, answer choice A is not correct. B) 13 Since 12 + 1 = 13, answer choice B is not correct. C) 14 Since we cannot get x + y to sum to 14, answer choice C is correct. Answer: C
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Re: When positive integer x is divided by 5, the remainder is 2.
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11 Feb 2019, 20:25
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Doubt regarding 0 being a postivei number
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07 May 2019, 10:13
While solving the Number Properties Manhattan book, I came across this question.
When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following values CANNOT be the sum x+y? A 12 B 13 C 14 D 16 E 21
Now the question is fairly straightforward. My doubt is regarding how come we are eliminating answer choice B i.e. 13. It is a possible value of x + y + 3 (remainder) as it can be 5 x 2 + 4 x 0 + 3, but the question has defined x and y to be positive integers only i.e. whole numbers greater than 0.
Hope by doubt is clear  Can someone explain to me how they eliminated Answer Choice B.



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Doubt regarding 0 being a postivei number
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07 May 2019, 10:42
naturalthing wrote: While solving the Number Properties Manhattan book, I came across this question.
When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following values CANNOT be the sum x+y? A 12 B 13 C 14 D 16 E 21
Now the question is fairly straightforward. My doubt is regarding how come we are eliminating answer choice B i.e. 13. It is a possible value of x + y + 3 (remainder) as it can be 5 x 2 + 4 x 0 + 3, but the question has defined x and y to be positive integers only i.e. whole numbers greater than 0.
Hope by doubt is clear  Can someone explain to me how they eliminated Answer Choice B. Hi, When you consider possible cases for x you can assume values to be 2,7,12,17 etc and when you consider the same case for y you can assume values to be 1,5,9,13,17 etc. Now when you take x=12 and y=1 you get the value as 13. Hope this helps




Doubt regarding 0 being a postivei number
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07 May 2019, 10:42






