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10! is divisible
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Updated on: 26 Mar 2018, 09:28
Updated on: 26 Mar 2018, 09:28
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Question Stats:
62% (00:48) correct
37% (01:01) wrong based on 24 sessions
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10! is divisible by \(3^x5^y\), where x and y are positive integers
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.
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.
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
Given Kudos: 0
Re: Quantitative Reasoning
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Updated on: 03 Apr 2018, 09:48
Updated on: 03 Apr 2018, 09:48
2
Expert Reply
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.
Using similar logic, we know that 5 and 10 have factors of 5, so y must be 2. Thus, the answer is A.
Originally posted by SherpaPrep on 14 Mar 2018, 23:58.
Last edited by SherpaPrep on 03 Apr 2018, 09:48, edited 1 time in total.
Last edited by SherpaPrep on 03 Apr 2018, 09:48, edited 1 time in total.
Re: Quantitative Reasoning
[#permalink]
15 Mar 2018, 01:34
15 Mar 2018, 01:34
1
Expert Reply
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://gre.myprepclub.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
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://gre.myprepclub.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 questionRegards
while I was right
