|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 09 Feb 2013
Posts: 122
Followers: 1
Kudos [?]:
70
[0], given: 17
|
If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
 15 Feb 2013, 12:24
Question Stats:
44% (01:22) correct
56% (00:25) wrong based on 50 sessions
If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end? A. 16 B. 17 C. 18 D. 19 E. 20
_________________
Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.
Last edited by Bunuel on 16 Feb 2013, 03:44, edited 1 time in total.
Edited the OA.
|
|
|
|
|
|
|
Manager
Status: Helping People Ace the GMAT
Affiliations: GMAT Prepster and Stratus Prep
Joined: 16 Jan 2013
Posts: 142
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 770 Q50 V46
GPA: 3.1
WE: Consulting (Consulting)
Followers: 5
Kudos [?]:
36
[3] , given: 4
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
15 Feb 2013, 12:34
3
This post received
KUDOS
2 x 5 gives you a zero at the end of the number. This means you are only looking for additional 5s (there are plenty of factors of 2 in 73! 75 has 2 5s and 80 has 1. So, there should be 3 more (this means that the answer is actually 19. What is the source of your question?
_________________
If my response helps, please add throw me a kudos.
Jim Kernan is the Director of GMAT Operations at Stratus Prep and author of GMAT Materials for GMAT Prepster.
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3173
Location: Pune, India
Followers: 598
Kudos [?]:
2129
[0], given: 97
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
15 Feb 2013, 19:15
emmak wrote: If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end?
A. 16
B. 17
C. 18
D. 19
E. 20 Are these questions from a test? The OA given is (D), not (C)
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10135
[3] , given: 965
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
16 Feb 2013, 03:51
3
This post received
KUDOS
emmak wrote: If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end?
A. 16
B. 17
C. 18
D. 19
E. 20 We can solve the question using info given in the stem (about 73!) but I find it easier to use direct approach of trailing zeros. Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. 125000 has 3 trailing zeros; The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: \frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^(k+1)>nIt's more simple if you look at an example: How many zeros are in the end (after which no other digits follow) of 32!? \frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less) So there are 7 zeros in the end of 32! The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero. BACK TO THE ORIGINAL QUESTION:According to above 80! has \frac{80}{5}+\frac{80}{25}=16+3=19 trailing zeros (take only the quotient into account). Answer: D. For more on trailing zeros check: everything-about-factorials-on-the-gmat-85592-40.htmlSimilar questions to practice: if-60-is-written-out-as-an-integer-with-how-many-101752.htmlhow-many-zeros-does-100-end-with-100599.htmlfind-the-number-of-trailing-zeros-in-the-expansion-of-108249.htmlfind-the-number-of-trailing-zeros-in-the-product-of-108248.htmlif-n-is-the-product-of-all-multiples-of-3-between-1-and-101187.htmlif-m-is-the-product-of-all-integers-from-1-to-40-inclusive-108971.htmlif-p-is-a-natural-number-and-p-ends-with-y-trailing-zeros-108251.htmlif-10-2-5-2-is-divisible-by-10-n-what-is-the-greatest-106060.htmlp-and-q-are-integers-if-p-is-divisible-by-10-q-and-cannot-109038.htmlquestion-about-p-prime-in-to-n-factorial-108086.htmlif-n-is-the-product-of-integers-from-1-to-20-inclusive-106289.htmlwhat-is-the-greatest-value-of-m-such-that-4-m-is-a-factor-of-105746.htmlif-d-is-a-positive-integer-and-f-is-the-product-of-the-first-126692.htmlif-10-2-5-2-is-divisible-by-10-n-what-is-the-greatest-106060.htmlHope 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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 14 Feb 2013
Posts: 31
Followers: 0
Kudos [?]:
7
[0], given: 14
|
If 73! has 16 zeroes at the end, how many zeroes will 80! ha [#permalink]
02 May 2013, 01:44
If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end? 1. 16 2. 17 3. 18 4. 19 5. 20
_________________
Consider giving +1 Kudo  when my post helps you.
Also, Good Questions deserve Kudos..!
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10135
[0], given: 965
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! ha [#permalink]
02 May 2013, 02:19
|
|
|
|
|
|
Intern
Joined: 03 Feb 2011
Posts: 4
Followers: 0
Kudos [?]:
0
[0], given: 5
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
03 May 2013, 15:29
Nice conceptual thinking by Jim. Faster way to solve.
|
|
|
|
|
|
Intern
Joined: 13 Dec 2012
Posts: 5
Followers: 0
Kudos [?]:
2
[0], given: 0
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80! [#permalink]
06 May 2013, 19:05
A tougher question wouldn't have the comment 73! so I chose to handle this one head on, that is, looking for the number of 0's that can be constructed from 80!
Prime Factoring: you need a 2 and a 5 to make a 10 (a "zero"), and there are TONS of 2's so let's skip these and focus on the (rarer) 5s:
80! = 1*2*3*4*5*6...*78*79*80
Since there are 80 consecutive numbers, there are 16 multiples of 5 in there, but if we're prime factoring, we need to remember that SOME multiples of 5 actually contain more than just one 5. Which? 25 comes to mind -- it's got two of them! So all the multiples of 25 actually contain two 5's (ie: 50 and 75)
So, to recap, we have 16 of them, plus 3 more (the additional 5's in 25, 50, and 75), so that makes 19, and since we have more than enough 2's, we know our number will have exactly 19 zeros at the end.
Hope this helps!
|
|
|
|
|
|
|
Re: If 73! has 16 zeroes at the end, how many zeroes will 80!
[#permalink]
06 May 2013, 19:05
|
|
|
|
|
|
|
|
|
|
|
close
