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# Even Tougher Number Properties....

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Current Student
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Even Tougher Number Properties.... [#permalink]  11 Oct 2005, 17:01
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math-2.doc [54.5 KiB]

SVP
Joined: 24 Sep 2005
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Kudos [?]: 94 [0], given: 0

the product of first 8 positive integers is 1.2.......8 , this includes 2.4.8= 64 ---> (1) is ok.
(1) a^n= 64, there are several cases:
2^6, 4^3, 8^2 ----> (1) alone is insuff
(2) n=6 , say nothing
if (1) and (2) together, a^6=64---> a=2
C?
Director
Joined: 21 Aug 2005
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1.) Insuff.
can be 2^6 or 8^2 both 2 and 8 divide the product of 1st 8 numbers
2.) Insuff.

Together, we can say a=2 as n=6

So C
Senior Manager
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Product of first 8 numbers give 2^7 * 3 ^ 2 * 5 * 7

1. Has multiple choices

2. I ignored because it would take time to calc something power 6

So I concluded the answer to be C

Can we really ignore stmt 2 or we are ignoring just because of complex calculation (or) can it be proven that it has many possibilites?
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I get B. This is why.

1. insuff. a^n=64, a=n=8 or a=2 n=6

2. suff. Because we know that 8! is multiple of a^n means that 8! has to be evenly divided by a^n. If n=6 and we know that a>1, then we know that a=2 for 8! to be divisible by a^n. I broke it down like this:

8*7*6*5*4*3*2*1=b(a^6), where b is some multiple and it has to be an integer for it to be a multiple. If a=2, then 8! is evenly divided by 2^6, but any number above 2 will not work.

What is the OA and OE?
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Christopher Wilson

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Re: B [#permalink]  12 Oct 2005, 05:35
chriswil2005 wrote:
I get B. This is why.

1. insuff. a^n=64, a=n=8 or a=2 n=6

2. suff. Because we know that 8! is multiple of a^n means that 8! has to be evenly divided by a^n. If n=6 and we know that a>1, then we know that a=2 for 8! to be divisible by a^n. I broke it down like this:

8*7*6*5*4*3*2*1=b(a^6), where b is some multiple and it has to be an integer for it to be a multiple. If a=2, then 8! is evenly divided by 2^6, but any number above 2 will not work.

What is the OA and OE?

great job! I didn't see through this. Thank you!!
Current Student
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OA is B...

Chris if you can do this problem...you will score 48+ on the real exam...
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ha [#permalink]  12 Oct 2005, 06:26
fresinha. Thanks for the encouragement. However, I have already taken that darn test (I vow to never say the name again) and I can't seem to get in the 40s. Practice tests, sure no problem, but the real test just makes me nervous.

I take the test again in couple weeks.
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Christopher Wilson

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I had a small hunch that n=6, would give some clue, however I did not attack the problem in these lines.

My 2 cents: Be confident & do not get nervous, you would score high.
Current Student
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Re: ha [#permalink]  12 Oct 2005, 13:11
this time it will be different....

look I scored 49 Q on this CAT, and this was one of the hardest problems on it...so if you can do this...you are going to score high...trust me....

chriswil2005 wrote:
fresinha. Thanks for the encouragement. However, I have already taken that darn test (I vow to never say the name again) and I can't seem to get in the 40s. Practice tests, sure no problem, but the real test just makes me nervous.

I take the test again in couple weeks.
Re: ha   [#permalink] 12 Oct 2005, 13:11
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