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If the integers a and n are greater than 1 and the product o

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If the integers a and n are greater than 1 and the product o [#permalink]

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New post 11 Oct 2005, 18:01
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If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-integers-a-and-n-are-greater-than-1-and-the-product-132382.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Jul 2014, 23:56, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 11 Oct 2005, 18:33
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?
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 11 Oct 2005, 19:15
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
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 11 Oct 2005, 23:01
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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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 12 Oct 2005, 06:30
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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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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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!!
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 12 Oct 2005, 07:14
OA is B...

Chris if you can do this problem...you will score 48+ on the real exam...
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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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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 12 Oct 2005, 08:00
Thanks for the answer chriswil2005.

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.
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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New post 12 Oct 2005, 14:11
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....

just dont loose your nerves....

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.
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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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Re: If the integers a and n are greater than 1 and the product o [#permalink]

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FN wrote:
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?

(1) a^n = 64

(2) n = 6


Prime factorization would be the best way to attack such kind of questions.

Given: \(a^n*k=8!=2^7*3^2*5*7\).
Question: \(a=?\)

(1) \(a^n=64=2^6=4^3=8^2\), so \(a\) could be 2, 4, or 8. Not sufficient.

(2) \(n=6\) --> the only integer (more than 1), which is a factor of 8!, and has the power of 6 (at least) is 2, hence \(a=2\). Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-integers-a-and-n-are-greater-than-1-and-the-product-132382.html
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Re: If the integers a and n are greater than 1 and the product o   [#permalink] 29 Jul 2014, 23:57
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