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When positive integer x is divided by 5, the remainder is 2. [#permalink]
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15 Jun 2014, 03:20
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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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Last edited by Bunuel on 15 Jun 2014, 03:40, 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. [#permalink]
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15 Jun 2014, 03:41
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. [#permalink]
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16 Jun 2014, 22:13
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Re: When positive integer x is divided by 5, the remainder is 2. [#permalink]
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20 Jun 2016, 19:54
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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. [#permalink]
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09 Nov 2016, 14:23
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. [#permalink]
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06 Sep 2017, 08:13
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. [#permalink]
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06 Sep 2017, 08:23
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. [#permalink]
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06 Sep 2017, 08:40
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. [#permalink]
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06 Sep 2017, 21:31
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. [#permalink]
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07 Sep 2017, 02:40
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. [#permalink]
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11 Sep 2017, 10:35
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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