n divisible by 4? (possible og 12th ed error)

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n divisible by 4? (possible og 12th ed error)

by carvv » Fri Jan 14, 2011 11:01 pm
Hello,

I'm using OG 12th edition to study, and I believe I may have found an error with DS problem 170 on page 349.

If n is a positive integer, is n^3 - n divisible by 4?

1) n = 2k + 1, where k is an integer.

2) n^2 + n is divisible by 6.

The book claims that the answer is A - statement 1 is sufficient. That seems incorrect. If you evaluate k as 0, n=1 as per statement 1. Then (1)^3 - 1 is not divisible by 4. However, you can clearly make the statement true by choosing a different k. Try k=2. n becomes 5, and n^3 - n is 120. 120 is divisible. One can make the statement true or false by choosing 1 or 2 for k, so statement 1 seems insufficient. There's no indication in statement 1 of k being positive, negative, or zero. So, it seems well within the bounds of the problem to chose either 0 or 1.

Am I missing something?
Source: — Data Sufficiency |

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by anshumishra » Fri Jan 14, 2011 11:07 pm
carvv wrote:Hello,

I'm using OG 12th edition to study, and I believe I may have found an error with DS problem 170 on page 349.

If n is a positive integer, is n^3 - n divisible by 4?

1) n = 2k + 1, where k is an integer.

2) n^2 + n is divisible by 6.

The book claims that the answer is A - statement 1 is sufficient. That seems incorrect. If you evaluate k as 0, n=1 as per statement 1. Then (1)^3 - 1 is not divisible by 4. However, you can clearly make the statement true by choosing a different k. Try k=2. n becomes 5, and n^3 - n is 120. 120 is divisible. One can make the statement true or false by choosing 1 or 2 for k, so statement 1 seems insufficient. There's no indication in statement 1 of k being positive, negative, or zero. So, it seems well within the bounds of the problem to chose either 0 or 1.

Am I missing something?
Yes, 0 is divisible by all the numbers except 0(for which the division is undefined) and hence by 4.
n^3 - n = (n-1)*n*(n+1) = even*odd*even , so divisible by 4.
Last edited by anshumishra on Sat Jan 15, 2011 8:05 am, edited 1 time in total.
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by arora007 » Sat Jan 15, 2011 7:45 am
just if i could add one more bit...

0 is divisible by all the numbers except itself.

any number divided by zero is undefined!
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by anshumishra » Sat Jan 15, 2011 8:04 am
arora007 wrote:just if i could add one more bit...

0 is divisible by all the numbers except itself.

any number divided by zero is undefined!
Thanks arora007.
Perfect. Let me edit my post.
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by carvv » Mon Jan 17, 2011 3:17 pm
Thanks a lot, guys! I hadn't considered that 0 was divisible by 4. That was the missing link for me.