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# 10! is divisible

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10! is divisible [#permalink]  14 Mar 2018, 22:49
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50% (00:40) correct 50% (01:01) wrong based on 18 sessions
10! is divisible by $$3^x5^y$$, where x and y are positive integers

 Quantity A Quantity B The greatest possible value for x The greatest possible value for y

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 26 Mar 2018, 09:28, edited 3 times in total.
Edited by Carcass
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Re: Quantitative Reasoning [#permalink]  14 Mar 2018, 23:58
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10! means 10x9x8x7x6x5x4x3x2x1. Just getting that out of the way. So if we want to know the maximum value of x, we basically need to count up how many 3s there are in 10!. Every third integer is divisible by 3, so that's 3, 6, and 9. It's a trap to think you're done here. We should also realize that every ninth integer is divisible by 9, and 9 has two 3s as factors. In other words, 9 should count twice. So x = 4, not 3.

Using similar logic, we know that 5 and 10 have factors of 5, so y must be 2. Thus, the answer is A.
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Last edited by SherpaPrep on 03 Apr 2018, 09:48, edited 1 time in total.
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Re: Quantitative Reasoning [#permalink]  15 Mar 2018, 01:34
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Dear away,

Following the rules is not easy but also is fundamental because for the other students is a straight forward way to find a question. Posting images do not help at all.

See this post how to post a question is a few and really simple steps. https://greprepclub.com/forum/qq-how-to ... -2357.html

However, I summarize for you what to do: post a question on the right forum for instance a numeric entry on the relative subforum, the title of the question should be the first sentence of the question for an easy search, with a comparison question use the tag quantity to set up the two in the proper manner, use the tags to identify the question as level of difficulty type and source.

It seems a lot of work but it is just 20 seconds.

@update look now how it appears I edited the question

Regards
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Re: Quantitative Reasoning [#permalink]  15 Mar 2018, 07:11
SherpaPrep wrote:
10! means 10x9x8x7x6x5x4x3x2x1. Just getting that out of the way. So if we want to know the maximum value of x, we basically need to count up how many 3s there are in 10!. Every third integer is divisible by 3, so that's 3, 6, and 9. It's a trap to think you're done here. We should also realize that every ninth integer is divisible by 9, and 9 has two 3s as factors. In other words, 9 should count twice. So x = 4, not 3.

Using similar logic, we know that 5 and 10 have factors of 5, so y must be 2. Thus, 2y = 4 and the answer is C.

Are u really sure ANS is C, I don't see "2y", where is it from?
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Re: 10! is divisible [#permalink]  15 Mar 2018, 15:58
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correct: A
we should write the number 10! into it's simplest form consisting of just prime numbers.
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = $$2^8 *3^4 * 5^2 * 7$$
10! = $$3^x * 5^y$$ so x = 4 and y = 2
so x is bigger than y

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Last edited by Carcass on 16 Mar 2018, 02:20, edited 1 time in total.
Edited by Carcass
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Re: 10! is divisible [#permalink]  16 Mar 2018, 03:40
How is the answer C? I am getting A. I have x = 4 and y = 2.
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Re: 10! is divisible [#permalink]  21 Mar 2018, 16:12
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The sad part of story is that I spent 10 minutes from my valuable time trying to prove me wrong while I was right
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Re: 10! is divisible [#permalink]  26 Mar 2018, 09:24
Please correct the OA of this question.

Choice A is correct.
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Re: 10! is divisible [#permalink]  26 Mar 2018, 09:29
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Done. Thank you guys for your collaboration.

However, next time posts like this one will be closed.

Regards
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Re: 10! is divisible   [#permalink] 26 Mar 2018, 09:29
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