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Re: If k is a positive integer and n = k(k+7)..... [#permalink]
02 Nov 2013, 21:08

2

This post was BOOKMARKED

Jem2905 wrote:

Hi guys, trying to get a little help on this problem that stumped me recently on a practice test. After going back and spending some more time with it, I got a different answer but I'm not sure if it's the right answer, and I'm not exactly sure I understand why it's the correct answer... any resphrasing of the question or statements will be hugely appreciated. Thanks!!

If k is a positive integer and n = k(k + 7k), is n divisible by 6?

(1) k is odd.

(2) When k is divided by 3, the remainder is 2.

Given, n= k(k+7K) = 8k^2 now for n to be divisible by 6, k should be divisible by 3.

1. K is odd. clearly insufficient, for k=1 answer is No. for k=3, answer is yes.

2. When k is divided by 3, the remainder is 2. Remainder is 2, so K can never be divisible by 3, Hence n will not be divisible by 6. So Sufficient.

Re: If k is a positive integer and n = k(k+7)..... [#permalink]
10 Nov 2013, 07:45

Chiranjeevee wrote:

Jem2905 wrote:

Hi guys, trying to get a little help on this problem that stumped me recently on a practice test. After going back and spending some more time with it, I got a different answer but I'm not sure if it's the right answer, and I'm not exactly sure I understand why it's the correct answer... any resphrasing of the question or statements will be hugely appreciated. Thanks!!

If k is a positive integer and n = k(k + 7k), is n divisible by 6?

(1) k is odd.

(2) When k is divided by 3, the remainder is 2.

Given, n= k(k+7K) = 8k^2 now for n to be divisible by 6, k should be divisible by 3.

1. K is odd. clearly insufficient, for k=1 answer is No. for k=3, answer is yes.

2. When k is divided by 3, the remainder is 2. Remainder is 2, so K can never be divisible by 3, Hence n will not be divisible by 6. So Sufficient.

IMO, B

Hi, I'm trying to understand this question too. The question I saw had n=K(K+7), not k+ 7K as written in the question above. Can anyone explain this q with the change please?

Re: If k is a positive integer and n = k(k+7)..... [#permalink]
10 Nov 2013, 11:30

7

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

ashsim wrote:

Chiranjeevee wrote:

Jem2905 wrote:

Hi guys, trying to get a little help on this problem that stumped me recently on a practice test. After going back and spending some more time with it, I got a different answer but I'm not sure if it's the right answer, and I'm not exactly sure I understand why it's the correct answer... any resphrasing of the question or statements will be hugely appreciated. Thanks!!

If k is a positive integer and n = k(k + 7k), is n divisible by 6?

(1) k is odd.

(2) When k is divided by 3, the remainder is 2.

Given, n= k(k+7K) = 8k^2 now for n to be divisible by 6, k should be divisible by 3.

1. K is odd. clearly insufficient, for k=1 answer is No. for k=3, answer is yes.

2. When k is divided by 3, the remainder is 2. Remainder is 2, so K can never be divisible by 3, Hence n will not be divisible by 6. So Sufficient.

IMO, B

Hi, I'm trying to understand this question too. The question I saw had n=K(K+7), not k+ 7K as written in the question above. Can anyone explain this q with the change please?

Thanks!

If k is a positive integer and n = k(k + 7), is n divisible by 6?

(1) k is odd. If \(k = 1\), then \(n = k(k + 7) = 8\) and n is NOT divisible by 6 but if \(k = 3\), then \(n = k(k + 7) = 30\) and n IS divisible by 6. Not sufficient.

(2) When k is divided by 3, the remainder is 2 --> \(k = 3x + 2\) --> \(n = k(k + 7) = (3x + 2)(3x + 9)=9x^2+33 x+18=3(3x^2+11x)+18\). Notice that \(3x^2+11x\) is even no matter whether x is even or odd, thus \(n=3(3x^2+11x)+18=3*even+(a \ multiple \ of \ 6)=(a \ multiple \ of \ 6)+(a \ multiple \ of \ 6)=(a \ multiple \ of \ 6)\). Sufficient.

Re: If k is a positive integer and n = k(k+7)..... [#permalink]
10 Nov 2013, 14:41

Quote:

If k is a positive integer and n = k(k + 7), is n divisible by 6?

(1) k is odd. If \(k = 1\), then \(n = k(k + 7) = 8\) and n is NOT divisible by 6 but if \(k = 3\), then \(n = k(k + 7) = 30\) and n IS divisible by 6. Not sufficient.

(2) When k is divided by 3, the remainder is 2 --> \(k = 3x + 2\) --> \(n = k(k + 7) = (3x + 2)(3x + 9)=9x^2+33 x+18=3(3x^2+11x)+18\). Notice that \(3x^2+11x\) is even no matter whether x is even or odd, thus \(n=3(3x^2+11x)+18=3*even+(a \ multiple \ of \ 6)=(a \ multiple \ of \ 6)+(a \ multiple \ of \ 6)=(a \ multiple \ of \ 6)\). Sufficient.

Re: If k is a positive integer and n = k(k+7)..... [#permalink]
11 Nov 2013, 02:23

4

This post received KUDOS

Here is my solution- If n=K(K+7), then-

1) k is odd => odd * (odd + Even) = Odd * Odd. We can not say it is multiple of 6 or not. Insufficient. 2) k = 3m +2. So, n=K(K+7) => n= (3m+2)(3m+9)= 3(3m+2)(m+3) => multiple of 3. If m is odd, m+3 is even. Hence , multiple of 2. Also it is a multiple of 3 => multiple of 6 If m is even, 3m+2 is even. Hence , multiple of 2. Also it is a multiple of 3 => multiple of 6 So B is sufficient.

Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink]
09 Apr 2014, 15:51

I still don't see why Statement 2 is Sufficient. If you use 5, the outcome is 60 (divisible by 60), and if you use 8 the outcome is 320 (not divisible by 6). Please explain.

Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink]
10 Apr 2014, 01:22

Expert's post

jbartuccio wrote:

I still don't see why Statement 2 is Sufficient. If you use 5, the outcome is 60 (divisible by 60), and if you use 8 the outcome is 320 (not divisible by 6). Please explain.

If k=8, then n=k(k+7)=8*15=120, not 320 and 120 is divisible by 6.

Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink]
10 Apr 2014, 01:58

jbartuccio wrote:

I still don't see why Statement 2 is Sufficient. If you use 5, the outcome is 60 (divisible by 60), and if you use 8 the outcome is 320 (not divisible by 6). Please explain.

if you refer to the initial question: n= k(k+7k) = 8k^2

Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink]
02 Feb 2015, 18:38

ricsingh wrote:

jbartuccio wrote:

I still don't see why Statement 2 is Sufficient. If you use 5, the outcome is 60 (divisible by 60), and if you use 8 the outcome is 320 (not divisible by 6). Please explain.

if you refer to the initial question: n= k(k+7k) = 8k^2

Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink]
02 Feb 2015, 21:29

Expert's post

1

This post was BOOKMARKED

Jem2905 wrote:

If k is a positive integer and n = k(k + 7), is n divisible by 6?

(1) k is odd.

(2) When k is divided by 3, the remainder is 2.

Given: n = k(k + 7) Question: Is n divisible by 6?

(1) k is odd. If k = 1, n = 8 - Not divisible by 6 If k = 6, n is divisible by 6 Not sufficient

(2) When k is divided by 3, the remainder is 2. k = (3b+2) n = (3b+2)(3b+2 + 7) = (3b + 2)(3b + 9) = 3*(3b + 2)(b + 3) For n to be divisible by 6, it must be divisible by both 2 and 3. We see that it is divisible by 3. Let's see if it is divisible by 2 too i.e. if it is even. b can be odd or even in this expression. If it is odd, (b+3) will become even because (Odd + Odd = Even). If it is even, (3b+2) will become even because (Even + Even = Even). So in either case, n will be even. So n will be divisible by 3 as well as 2 i.e. it will be divisible by 6. Sufficient alone.

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