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What is the largest power of 3 contained in 200!

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What is the largest power of 3 contained in 200! [#permalink] New post 24 Oct 2010, 10:29
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Question Stats:

84% (01:56) correct 16% (01:08) wrong based on 242 sessions
What is the largest power of 3 contained in 200!

A. 88
B. 48
C. 66
D. 97
E. 39

If you think this question is really a challenge for you and you appreciate this kind of question then consider giving me some KUDOS......
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 07:53, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Can you take this challenge - 700+ quant [#permalink] New post 24 Oct 2010, 10:36
vyassaptarashi wrote:
Try this 700+ level question

Q. What is the largest power of 3 contained in 200!

A. 88
B. 48
C. 66
D. 97
E. 39

Send me the replies people. I will provide you the official answer and method soon.


If you think this question is really a challenge for you and you appreciate this kind of question then consider giving me some KUDOS......



Answer = \(\frac{200}{3} + \frac{200}{3^2} + \frac{200}{3^3} + \frac{200}{3^4}\)
= \(66+ 22 + 7 + 2 = 97\)

D
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Re: Can you take this challenge - 700+ quant [#permalink] New post 24 Oct 2010, 10:37
Expert's post
vyassaptarashi wrote:
Try this 700+ level question

Q. What is the largest power of 3 contained in 200!

A. 88
B. 48
C. 66
D. 97
E. 39

Send me the replies people. I will provide you the official answer and method soon.




If you think this question is really a challenge for you and you appreciate this kind of question then consider giving me some KUDOS......


Check this: everything-about-factorials-on-the-gmat-85592.html

So for this problem:

\(\frac{200}{3}+\frac{200}{3^2}+\frac{200}{3^3}+\frac{200}{3^4}=66+22+7+2=97\).

Answer: D.

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Hope it helps.
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Re: Can you take this challenge - 700+ quant [#permalink] New post 24 Jul 2013, 13:18
How did you know to stop at 200/3^4 and what is the theory behind this. I have been trying all of the questions you have on the put on here, but I guess i do not understand the theory behind this. Could you elaborate?

Thanks,
AK
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Re: Can you take this challenge - 700+ quant [#permalink] New post 24 Jul 2013, 13:20
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anujkhatiwada wrote:
How did you know to stop at 200/3^4 and what is the theory behind this. I have been trying all of the questions you have on the put on here, but I guess i do not understand the theory behind this. Could you elaborate?

Thanks,
AK


Link to theory was provided above: Check this: everything-about-factorials-on-the-gmat-85592.html
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Re: What is the largest power of 3 contained in 200! [#permalink] New post 13 Aug 2014, 11:59
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Re: What is the largest power of 3 contained in 200! [#permalink] New post 08 Dec 2015, 11:03
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Re: What is the largest power of 3 contained in 200! [#permalink] New post 09 Dec 2015, 11:05
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Hi All,

These types of questions don't require a complex math approach - they can be solved with a bit of 'brute force' and logic.

In real basic terms, we're asked to find all of the '3s' in 200!

We can figure out that 200/3 = 66, so we know that there are at least 66 '3s' in 200! While that answer is among the 5 choices, it seems a bit too 'easy', so let's do a bit more work and list out the first few numbers that we know have a '3' in them:

3 = 3x1
6 = 3x2
9 = 3x3

Notice how both 3 and 6 have just one 3 in them, but 9 has TWO 3s (there's an 'extra' 3 that we have to account for). This implies that there are probably other numbers that include 'extra 3s' that we have to figure out:

To find those extra 3s, we have to look at numbers that contain 'powers of 3'...

3^2 = 9
3^3 = 27
3^4 = 81

3^5 = 243, but that's too big (we're only going up to 200). Keep in mind that a multiple of 81 is also a multiple of 9 and 27, so we don't want to count any of those values more than once.

200/9 = 22, so we know that there are at least 22 extra 3s (and certainly more because of the 27 and 81). With the 66 3s that we already have, those 22 extra 3s increase the total to 88. With the other extra 3s, we'll end up with MORE than 88 3s. There's only one answer that fits that logic...

Final Answer:
[Reveal] Spoiler:
D


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Re: What is the largest power of 3 contained in 200!   [#permalink] 09 Dec 2015, 11:05
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