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

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If k is a positive integer and n = k(k + 7k), is n divisible [#permalink] New post 02 Nov 2013, 13:01
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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.
[Reveal] Spoiler: OA

Last edited by AbhiJ on 10 Apr 2014, 05:42, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 02 Nov 2013, 21:08
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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
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 04 Nov 2013, 16:51
What about 5? It is a positive integer, when divided by 3 the remainder is 2 and 5(5+7)= 5(12) = 60, divisible by 6.
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 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?

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

Answer: B.

Hope it's clear.
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 10 Nov 2013, 14:41
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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.

Answer: B.

Hope it's clear.


Thanks, that helps! :)
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 11 Nov 2013, 02:23
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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.
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 07 Jan 2014, 14:01
Hey guys,

I still have a question on this problem, can someone explain why my solution is incorrect?

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

1. K is odd

Test cases:
K=1 n=1(1+7) = 8, is 8/6 NO
K=3 n=3(3+7)=30, is 30/6 YES
INSUFFICIENT

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

Test Cases:
K=1 1/3=0 remainder 2, n=1(1+7) = 8, is 8/6 NO
K=5 5/3 =1 remainder 2, n=5(5+7) =60, is 60/6 YES
INSUFFICIENT

Combined:
K=1 overlaps - NO
K=5 overlaps - YES

I see the math approach in the posts above but why would the test cases produce a different result? What am I missing here?

Thanks in advance.
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Re: If k is a positive integer and n = k(k+7)..... [#permalink] New post 08 Jan 2014, 02:49
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msbandi4321 wrote:
Hey guys,

I still have a question on this problem, can someone explain why my solution is incorrect?

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

1. K is odd

Test cases:
K=1 n=1(1+7) = 8, is 8/6 NO
K=3 n=3(3+7)=30, is 30/6 YES
INSUFFICIENT

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

Test Cases:
K=1 1/3=0 remainder 2, n=1(1+7) = 8, is 8/6 NO
K=5 5/3 =1 remainder 2, n=5(5+7) =60, is 60/6 YES
INSUFFICIENT

Combined:
K=1 overlaps - NO
K=5 overlaps - YES

I see the math approach in the posts above but why would the test cases produce a different result? What am I missing here?

Thanks in advance.


1 divided by 3 yields the remainder of 1, not 2: 1=0*3+1.

Does this make sense?
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Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink] New post 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.
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Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink] New post 10 Apr 2014, 01:22
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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.

The reason why the second statement is sufficient is given here: if-k-is-a-positive-integer-and-n-k-k-7k-is-n-divisible-162594.html#p1290699 Does it make sense?
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If k is a positive integer and n = k(k + 7k), is n divisible [#permalink] New post 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

Hence, if k = 5, n = 8*5*5
if k = 8, n = 8*8*8

both of them are clearly not divisible by 6.

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