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What is the greatest integer m for which the

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What is the greatest integer m for which the [#permalink] New post 28 Nov 2013, 06:24
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What is the greatest integer m for which the number 50!/10^m is an integer?

(A) 5
(B) 8
(C) 10
(D) 11
(E) 12
[Reveal] Spoiler: OA
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Re: What is the greatest integer m for which the [#permalink] New post 29 Nov 2013, 01:51
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Expert's post
mohnish104 wrote:
What is the greatest integer m for which the number 50!/10^m is an integer?

(A) 5
(B) 8
(C) 10
(D) 11
(E) 12


Basically we need to find the number of trailing zeros in 50!.

50/5 + 50/5^2 = 10 + 2 = 12. (check here: everything-about-factorials-on-the-gmat-85592.html).

Answer: E.
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Re: What is the greatest integer m for which the [#permalink] New post 28 Nov 2013, 22:51
Expert's post
mohnish104 wrote:
What is the greatest integer m for which the number 50!/10^m is an integer?

(A) 5
(B) 8
(C) 10
(D) 11
(E) 12


Here is a conceptual discussion on this question: http://www.veritasprep.com/blog/2011/06 ... actorials/


As for 50!/10^m, the greatest value of m will be obtained by finding the maximum number of 5s in 50!

The quick process for that (discussed in the link above) is
50/5 = 10
10/5 = 2
Total number of 5s is 12. So maximum value of m will also be 12.
Answer (E)
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Re: What is the greatest integer m for which the [#permalink] New post 29 Nov 2013, 00:12
mohnish104 wrote:
What is the greatest integer m for which the number 50!/10^m is an integer?

(A) 5
(B) 8
(C) 10
(D) 11
(E) 12



10 = 5 x 2; 2s are in abundance so all we need is to count the number of 5s in 50! and get to the answer.

50! = 1 x 2 x 3 x ....50

5, 10, 15, 20, 25, 25, 30, 35, 40, 45, 50, 50

25 and 50 come twice because they have 2 fives.

There are 12 fives hence the highest 10 power is 12.

The answer is E.

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Re: What is the greatest integer m for which the [#permalink] New post 29 Nov 2013, 01:51
Expert's post
Bunuel wrote:
mohnish104 wrote:
What is the greatest integer m for which the number 50!/10^m is an integer?

(A) 5
(B) 8
(C) 10
(D) 11
(E) 12


Basically we need to find the number of trailing zeros in 50!.

50/5 + 50/5^2 = 10 + 2 = 12. (check here: everything-about-factorials-on-the-gmat-85592.html).

Answer: E.


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Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the greatest integer m for which the [#permalink] New post 26 Feb 2014, 13:32
Question can be asked as , if 10^m is a factorial of 50!, what is the greatest integer?

My version of answer is:
We can write 10^m = 2^m . 5^m
We can only get 10 when we multiply with 5, so if we solve this problem for 5, we get answer.
As we know formula n/x + n/x^1 + n/x^3 ...until x^k <= n

=> 50/5 + 50/5^2 => 10 + 2 => 12


*(if you are curious, you can solve for 2 also, 50/2 + 50/ 2^1 + 50/2^3 => 25+12+6 =>43. This number is greater than 12. And also you can make only 12 10's , that's the reason to consider 5 )
Re: What is the greatest integer m for which the   [#permalink] 26 Feb 2014, 13:32
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