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When positive integer k is divided by 6 the remainder is 3
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Updated on: 08 Feb 2016, 11:32
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When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer? a. k + 1 b. k 11 c. 4k + 2 d. (k3)/3 +2 e. k/3
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Originally posted by paisaj87 on 08 Feb 2016, 09:02.
Last edited by paisaj87 on 08 Feb 2016, 11:32, edited 2 times in total.



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Re: When positive integer k is divided by 6 the remainder is 3
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08 Feb 2016, 10:15
First, because k/6 leaves a remainder of 3, we know k must be odd. (k=6x+3 = 3(2x+1) = odd*odd = odd) Knowing k is odd we can examine the answer choices: a. k + 1 > odd + 1 > must be evenb. k 11 > odd  odd > must be evenc. 4k + 1 > 4*odd + 1 = even + 1 > must be oddd. (k3)/3 +2 > (6x+33)/3 + 2 = 2x + 2 > must be evene. k/3 > (6x+3)/3 = 2x+1 = Must be odd It seems we have a problem with the answer choices... Both C and E CANNOT result in an even integer. paisaj87  are you sure that these are the correct answer choices? What is the source of the problem?
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Re: When positive integer k is divided by 6 the remainder is 3
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08 Feb 2016, 11:33
Thnak you for your observation, answer choice c had a typo. davedekoos wrote: First, because k/6 leaves a remainder of 3, we know k must be odd. (k=6x+3 = 3(2x+1) = odd*odd = odd) Knowing k is odd we can examine the answer choices: a. k + 1 > odd + 1 > must be evenb. k 11 > odd  odd > must be evenc. 4k + 1 > 4*odd + 1 = even + 1 > must be oddd. (k3)/3 +2 > (6x+33)/3 + 2 = 2x + 2 > must be evene. k/3 > (6x+3)/3 = 2x+1 = Must be odd It seems we have a problem with the answer choices... Both C and E CANNOT result in an even integer. paisaj87  are you sure that these are the correct answer choices? What is the source of the problem?
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Re: When positive integer k is divided by 6 the remainder is 3
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08 Feb 2016, 11:33
Thnak you for your observation, answer choice c had a typo. davedekoos wrote: First, because k/6 leaves a remainder of 3, we know k must be odd. (k=6x+3 = 3(2x+1) = odd*odd = odd) Knowing k is odd we can examine the answer choices: a. k + 1 > odd + 1 > must be evenb. k 11 > odd  odd > must be evenc. 4k + 1 > 4*odd + 1 = even + 1 > must be oddd. (k3)/3 +2 > (6x+33)/3 + 2 = 2x + 2 > must be evene. k/3 > (6x+3)/3 = 2x+1 = Must be odd It seems we have a problem with the answer choices... Both C and E CANNOT result in an even integer. paisaj87  are you sure that these are the correct answer choices? What is the source of the problem?
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Re: When positive integer k is divided by 6 the remainder is 3
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08 Feb 2016, 14:21
paisaj87 wrote: When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
a. k + 1 b. k 11 c. 4k + 2 d. (k3)/3 +2 e. k/3 Another approach is to TEST values. When positive integer k is divided by 6 the remainder is 3So, k could equal 3, 9, 15, 21, etc let's TEST k = 3a. 3 + 1 = 4 (EVEN) b. 3 11 = 8 (EVEN) c. 4( 3) + 2 = 14 (EVEN) d. ( 33)/3 +2 = 2 (EVEN) At this point, we can already see the answer must be E. Let's check E for "fun" e. 3/3 = 1 (ODD) Great! Answer: E Cheers, Brent
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When positive integer k is divided by 6 the remainder is 3
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14 May 2018, 23:42
Is there any better approach than plugging numbers here? I spent quite a few time after arriving to below step: k = 6* Quotient + 3 (remainder)
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Re: When positive integer k is divided by 6 the remainder is 3
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15 May 2018, 00:35
paisaj87 wrote: When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
a. k + 1 b. k 11 c. 4k + 2 d. (k3)/3 +2 e. k/3 First step should be to find the value of k.
So from question we know that k = 3,9,15,21 .....
Plug k = 15 in answer choices
You will get :
A. 15+1 = 16
B. 1511 = 4
C. 4*15+2 = 62
D. (15  3)/3 + 2 = 6
E. 15/3 = 5
Hence E.
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Re: When positive integer k is divided by 6 the remainder is 3
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15 May 2018, 01:09
I feel the approach by davedekoos is nice one without plugging numbers... (PS: while relying to your post, I mistakenly edited it .) adkikani wrote: Is there any better approach than plugging numbers here? I spent quite a few time after arriving to below step:
k = 6* Quotient + 3 (remainder)
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When positive integer k is divided by 6 the remainder is 3
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15 May 2018, 01:09
adkikani wrote: Is there any better approach than plugging numbers here? I spent quite a few time after arriving to below step:
k = 6* Quotient + 3 (remainder) hi adkikanionce you have arrived at k=6*Q+3, you need to realize that k is odd because 6Q is even and 3 is odd, Hence even+odd=odd Now Odd divided by Odd is ODD / Non Even Integer. Hence straight option E



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When positive integer k is divided by 6 the remainder is 3
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15 May 2018, 06:26
adkikani wrote: Is there any better approach than plugging numbers here? I spent quite a few time after arriving to below step:
k = 6* Quotient + 3 (remainder) Here's a different approach: GIVEN: When positive integer k is divided by 6 the remainder is 3So, we can say that k = 6n + 3 for some integer n Now go to the answer choices and replace k with 6n+3.... a. k + 1 = 6n+3 + 1 = 6n + 4 = 2(3n + 2). We can see that this expression is a multiple of 2. ELIMINATE A b. k 11 = 6n+3  11 = 6n  8 = 2(3n  4). We can see that this expression is a multiple of 2. ELIMINATE B c. 4k + 2 = 4( 6n+3) + 2 = 24n + 14 = 2(12n + 7). We can see that this expression is a multiple of 2. ELIMINATE C) d. (k3)/3 +2 = ( 6n+3  3)/3 + 2 = 6n/3 + 2 = 2n + 2 = 2(n + 1). We can see that this expression is a multiple of 2. ELIMINATE D e. k/3 = ( 6n+3)/3 = 2n + 1. Since we know that 2n is EVEN, it must be the case that 2n+1 is ODD Answer: E Cheers, Brent
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Re: When positive integer k is divided by 6 the remainder is 3
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15 May 2018, 11:33
paisaj87 wrote: When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
a. k + 1 b. k 11 c. 4k + 2 d. (k3)/3 +2 e. k/3 Possible values of k are : 3 , 9 , 15 , 21................. a. k + 1 , if k = 3 and is divided by 6 result will be evenb. k 11 , if k = 15 and is divided by 6 result will be evenc. 4k + 2 , if k = 3 and is divided by 6 result will be evend. (k3)/3 +2 , if k = 3 and is divided by 6 result will be evene. k/3, (Any value of K will be completely divisible by 3 and will not produce even Integer...Answer must be (E)
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Re: When positive integer k is divided by 6 the remainder is 3
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21 Aug 2019, 06:32
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Re: When positive integer k is divided by 6 the remainder is 3
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