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What is the remainder when n is divided by 26, given that n divided by
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20 Oct 2015, 12:11
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62% (02:11) correct 38% (02:13) wrong based on 262 sessions
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What is the remainder when n is divided by 26, given that n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers) (1) a is odd (2) b = 3
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Re: What is the remainder when n is divided by 26, given that n divided by
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20 Oct 2015, 12:28
Bunuel wrote: What is the remainder when n is divided by 26, given that n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers)
(1) a is odd (2) b = 3 Target question: What is the remainder when n is divided by 26 Given: n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers) There's a nice rule that say, " If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 So, we can taken the given information and write: n = 13a + b Statement 1: a is odd There's no information about b, so it will be impossible to determine the remainder when divided by 26. Consider these two cases: Case a: a = 1 and b = 2. In this case, n = (13)(1) + 2 = 15, so n divided by 26 leaves a remainder of 15Case b: a = 1 and b = 3. In this case, n = (13)(1) + 3 = 16, so n divided by 26 leaves a remainder of 16Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: b = 3Consider these two contradictory cases: Case a: a = 2 and b = 3. In this case, n = (13)(2) + 3 = 29, so n divided by 26 leaves a remainder of 3Case b: a = 1 and b = 3. In this case, n = (13)(1) + 3 = 16, so n divided by 26 leaves a remainder of 16Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that a is odd, which means a = 2k + 1 for some integer k Statement 2 tells us that b = 3 So, let's take the given information ( n = 13a + b) and replace a with 2k + 1 and replace b with 3 to get: n = 13(2k + 1) + 3 = 26k + 13 + 3 = 26k + 16 Here we can see that n is 16 greater than some multiple of 26, so when we divide n by 26, the remainder will be 16Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent
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What is the remainder when n is divided by 26, given that n divided by
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Updated on: 20 Oct 2015, 13:41
Bunuel wrote: What is the remainder when n is divided by 26, given that n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers)
(1) a is odd (2) b = 3 n = 13a + b = 13(a1)+b +13 (1) a is odd => a  1 is even => 13(a1) is divisible by 26 => When n divided by 26, the remainder is 13+b We do not know the value of b so INSUFFICIENT (2) b = 3 => We do not know a is odd or even A is odd: the remainder: 13+b a is even: the remainder: b Insufficient (1) + (2) The remainder is 13+3 = 16 SUFFICIENT Ans: C
Originally posted by camlan1990 on 20 Oct 2015, 12:33.
Last edited by camlan1990 on 20 Oct 2015, 13:41, edited 1 time in total.



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Re: What is the remainder when n is divided by 26, given that n divided by
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20 Oct 2015, 13:24
GMATPrepNow wrote: Bunuel wrote: What is the remainder when n is divided by 26, given that n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers)
(1) a is odd (2) b = 3 Target question: What is the remainder when n is divided by 26 Given: n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers) There's a nice rule that say, " If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 So, we can taken the given information and write: n = 13a + b Statement 1: a is odd There's no information about b, so it will be impossible to determine the remainder when divided by 26. Consider these two cases: Case a: a = 1 and b = 2. In this case, n = (13)(1) + 2 = 15, so n divided by 26 leaves a remainder of 15Case b: a = 1 and b = 3. In this case, n = (13)(1) + 3 = 16, so n divided by 26 leaves a remainder of 16Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: b = 3Consider these two contradictory cases: Case a: a = 2 and b = 3. In this case, n = (13)(2) + 3 = 29, so n divided by 26 leaves a remainder of 3Case b: a = 1 and b = 3. In this case, n = (13)(1) + 3 = 16, so n divided by 26 leaves a remainder of 16Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that a is odd, which means a = 2k + 1 for some integer k Statement 2 tells us that b = 3 So, let's take the given information ( n = 13a + b) and replace a with 2k + 1 and replace b with 3 to get: n = 13(2k + 1) + 3 = 26k + 13 + 3 = 26k + 16 Here we can see that n is 16 greater than some multiple of 26, so when we divide n by 26, the remainder will be 16Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent Hi Brent, actually I wanted to place 2k+1 for St1+ST2, but what is with the case if our odd number=1 ? Can we always insert 2k+1 for an odd number ?
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Re: What is the remainder when n is divided by 26, given that n divided by
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20 Oct 2015, 13:31
BrainLab wrote: Hi Brent, actually I wanted to place 2k+1 for St1+ST2, but what is with the case if our odd number=1 ? Can we always insert 2k+1 for an odd number ? Yes, you can always insert 2k+1 for an odd integer. That is actually how we define an odd integer. Cheers, Brent
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Re: What is the remainder when n is divided by 26, given that n divided by
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29 Jun 2016, 10:39
GMATPrepNow wrote: BrainLab wrote: Hi Brent, actually I wanted to place 2k+1 for St1+ST2, but what is with the case if our odd number=1 ? Can we always insert 2k+1 for an odd number ? Yes, you can always insert 2k+1 for an odd integer. That is actually how we define an odd integer. Cheers, Brent Hello! wouldn't it be 2k1? in that sense 13(2k1) + 3 would not igual 16. I am confused about this because I read that the sequence of all positive odd integers is defined by An = 2N1. Would this matter for the solution of the problem? Thank you for your response. Greetings.
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Re: What is the remainder when n is divided by 26, given that n divided by
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29 Jun 2016, 11:06
Ilomelin wrote: GMATPrepNow wrote: BrainLab wrote: Hi Brent, actually I wanted to place 2k+1 for St1+ST2, but what is with the case if our odd number=1 ? Can we always insert 2k+1 for an odd number ? Yes, you can always insert 2k+1 for an odd integer. That is actually how we define an odd integer. Cheers, Brent Hello! wouldn't it be 2k1? in that sense 13(2k1) + 3 would not igual 16. I am confused about this because I read that the sequence of all positive odd integers is defined by An = 2N1. Would this matter for the solution of the problem? Thank you for your response. Greetings. 2k  1 is also an odd number for all integers k. However, if we use 2k1 here, we need to do a little extra work at the end. When we use 2k  1, we get: n = 13(2k  1) + 3 Simplify to get: n = 26k  10 In other words, n is 10 LESS than some multiple of 26 Hmmm, what does this tell us about the remainder when n is divided by 26? To find out, notice that we can take n = 26k  10 and rewrite is as n = 26(k  1 + 1)  10 Or..... n = 26(k  1) + 26  10 Simplify to get: n = 26(k1) +16 So, n is 16 GREATER than some multiple of 26 So, we when we divide n by 26, we get a remainder of 16 PRO TIP: use 2k + 1 when you need a nice generic odd number Cheers, Brent
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Re: What is the remainder when n is divided by 26, given that n divided by
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29 Jun 2016, 13:32
Bunuel wrote: What is the remainder when n is divided by 26, given that n divided by 13 gives “a” as the quotient and “b” as the remainder? (a, b and n are positive integers)
(1) a is odd (2) b = 3 n= 13a +b Statement 1= a is odd There is no information about b n= 13*1 +b n= 13*3 +b n= 13 *5 +b Not sufficient. Statement 2= b = 3 Multiple values possible. n= 3 n= 16 (13*1 +3) n= 29 (13*2+3) n= 42 (13*3 +3) Not sufficient. Combining both statements: When a is 1 (odd) and b= 3, let's say 16 then when n/26 will have 16 as remainder Similarly when n = 42  16 is remainder for n/26 C is the answer
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Re: What is the remainder when n is divided by 26, given that n divided by
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15 Nov 2018, 05:44
N=16(a=1(Odd) and b=3) then Remainder=16
N=42(a=3 & B=3) Then remainder=8
N=68(a=5 and b=3) then Remainder=8
As we are getting different remainders how the answer is C?



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Re: What is the remainder when n is divided by 26, given that n divided by
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19 Nov 2018, 05:05
anuppatle85 wrote: N=16(a=1(Odd) and b=3) then Remainder=16
N=42(a=3 & B=3) Then remainder=8
N=68(a=5 and b=3) then Remainder=8
As we are getting different remainders how the answer is C? I am wondering the same thing.. n = 13a + b St 1 + 2) > a = 1, 3, 5, 7 etc b = 3 n = 13a + 3 if a = 1, n = 16. 16/26 gives remainder 26! (because 26 does not go into 16, hence 16/26 is 0 remainder 26). if a = 3, n = 42. 42/26 gives remainder 16. if a = 5, n = 68. 68/26 gives remainder 16. We see that this will hold for all "A" greater than 1 and also odd.. so from 3 onwards. However, a = 1 is a possibility and this yields a different remainder. If someone could please provide an explanation that'd be great.



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What is the remainder when n is divided by 26, given that n divided by
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22 Mar 2019, 10:06
PierTotti17 wrote: anuppatle85 wrote: N=16(a=1(Odd) and b=3) then Remainder=16
N=42(a=3 & B=3) Then remainder=8
N=68(a=5 and b=3) then Remainder=8
As we are getting different remainders how the answer is C? I am wondering the same thing.. n = 13a + b St 1 + 2) > a = 1, 3, 5, 7 etc b = 3 n = 13a + 3 if a = 1, n = 16. 16/26 gives remainder 26! (because 26 does not go into 16, hence 16/26 is 0 remainder 26).if a = 3, n = 42. 42/26 gives remainder 16. if a = 5, n = 68. 68/26 gives remainder 16. We see that this will hold for all "A" greater than 1 and also odd.. so from 3 onwards. However, a = 1 is a possibility and this yields a different remainder. If someone could please provide an explanation that'd be great. The highlighted part is wrong: the remainder can only be a nonnegative integer that is less than the divisor. In the case of n=16, the divisor is 26. So it goes into it 0 times, thus the remainder is 16. Think about it like fractions... 16/26 is less than 1... 0 + 16/26 Comparatively, a=3 gives 42/26 which is 1 + 16/26 Check: https://gmatclub.com/forum/remainders144665.htmlhttps://www.veritasprep.com/blog/2011/0 ... yapplied/




What is the remainder when n is divided by 26, given that n divided by
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