Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47920

What is the value of N?
[#permalink]
Show Tags
09 Feb 2015, 06:42
Question Stats:
38% (01:29) correct 62% (01:18) wrong based on 252 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 47920

Re: What is the value of N?
[#permalink]
Show Tags
16 Feb 2015, 05:31
Bunuel wrote: What is the value of N?
(1) N! ends with 28 zeroes
(2) (N+2)! ends with 31 zeroes and (N1)! ends with 28 zeroes
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONIn any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5. Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us. Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor. Hence Statement 1 is not sufficient. As per Statement 2 the (N+2)! has 31 zeroes. So let’s check which numbers can have 30 zeroes. We know from the above that 120!124! should have 28 zeroes. But when it comes to 125!, we have 5^3 factor so 125!129! have 31 zeroes. So N+2 can be any number between 125 to 129, but the statement also says N1 has 28 zeroes that means N1 can be any number from 120! to 124!. So N can be 125 or 124 or 123 so again Statement 2 is not sufficient. Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 04 Oct 2013
Posts: 173
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

Re: What is the value of N?
[#permalink]
Show Tags
09 Feb 2015, 07:08
Bunuel wrote: What is the value of N?
(1) N! ends with 28 zeroes
(2) (N+2)! ends with 31 zeroes and (N1)! ends with 28 zeroes
Kudos for a correct solution. stastement 1: If N=124 > total number of zeroes=124/5+124/25=28. If N=123 > total number of zeroes=123/5+123/25=28. statement 2: works with both 123 and 124. 1+2) works with both 123 and 124. Answer E.
_________________
learn the rules of the game, then play better than anyone else.



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 520
Location: India

Re: What is the value of N?
[#permalink]
Show Tags
13 Feb 2015, 05:17
Hi all, Again a value DS question. 1). Statement 1 is insufficient. To find the number of zeros all we need is find number of five’s. For N values 120,121,122,123,124… the number of zeros(Number of five's) is 28 So insufficient 2). Statement 2 is insufficient. N values again can be 123,124,125… Together also insufficient, Because N can be 123 or 124. So answer is E
_________________
For more info on GMAT and MBA, follow us on @AskCrackVerbal



Math Expert
Joined: 02 Aug 2009
Posts: 6524

Re: What is the value of N?
[#permalink]
Show Tags
13 Feb 2015, 06:17
CrackVerbalGMAT wrote: Hi all, Again a value DS question. 1). Statement 1 is insufficient. To find the number of zeros all we need is find number of five’s. For N values 120,121,122,123,124… the number of zeros(Number of five's) is 28 So insufficient 2). Statement 2 is insufficient. N values again can be 123,124,125… Together also insufficient, Because N can be 123 or 124. So answer is E hi N cannot be 125.... because it is given N! has 28 zeroes in end..
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Math Expert
Joined: 02 Aug 2009
Posts: 6524

Re: What is the value of N?
[#permalink]
Show Tags
13 Feb 2015, 06:26
Bunuel wrote: What is the value of N?
(1) N! ends with 28 zeroes
(2) (N+2)! ends with 31 zeroes and (N1)! ends with 28 zeroes
Kudos for a correct solution. ans E.. firstly the value of zeroes depends on power of 5 as power of 2 will always be greater than power of 5... as we see (N+2)! increases the zeroes by 3 digits...it means between N and N+2, there is 5^3 multiple..125,250... here 125 fits in .. 1) statement one gives us values 120 to 124....as 119 will give 27 zeroes and 125 will give 31 zeroes.. insufficient.. 2) statement two gives us values 123 to 127 as N+2 < 130... insufficient.. combined two values still remain... 123 and 124.. insufficient
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Manager
Joined: 14 Jul 2014
Posts: 94

Re: What is the value of N?
[#permalink]
Show Tags
16 Feb 2015, 04:54
I dont understand why has everyone picked 124, 125 as the starting point for N
Not clear  Can somebody pls explain



Math Expert
Joined: 02 Sep 2009
Posts: 47920

Re: What is the value of N?
[#permalink]
Show Tags
16 Feb 2015, 05:33
Bunuel wrote: Bunuel wrote: What is the value of N?
(1) N! ends with 28 zeroes
(2) (N+2)! ends with 31 zeroes and (N1)! ends with 28 zeroes
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONIn any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5. Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us. Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor. Hence Statement 1 is not sufficient. As per Statement 2 the (N+2)! has 31 zeroes. So let’s check which numbers can have 30 zeroes. We know from the above that 120!124! should have 28 zeroes. But when it comes to 125!, we have 5^3 factor so 125!129! have 31 zeroes. So N+2 can be any number between 125 to 129, but the statement also says N1 has 28 zeroes that means N1 can be any number from 120! to 124!. So N can be 125 or 124 or 123 so again Statement 2 is not sufficient. Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer. For similiar questions check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory. Hope this helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Aug 2009
Posts: 6524

What is the value of N?
[#permalink]
Show Tags
16 Feb 2015, 05:46
buddyisraelgmat wrote: I dont understand why has everyone picked 124, 125 as the starting point for N
Not clear  Can somebody pls explain hi firstly the value of zeroes depends on power of 5 as power of 2 will always be greater than power of 5... as we see (N+2)! increases the zeroes by 3 digits...it means between N and N+2, there is 5^3 multiple..125,250... here 125 fits in .. because no of zeroes=125/5+125/5^2+125/5^3=25+5+1=31...
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 26 Nov 2014
Posts: 7

Re: What is the value of N?
[#permalink]
Show Tags
10 Mar 2015, 12:21
Bunuel wrote: Bunuel wrote: What is the value of N?
(1) N! ends with 28 zeroes
(2) (N+2)! ends with 31 zeroes and (N1)! ends with 28 zeroes
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONIn any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5. Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us. Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor. Hence Statement 1 is not sufficient. As per Statement 2 the (N+2)! has 31 zeroes. So let’s check which numbers can have 30 zeroes. We know from the above that 120!124! should have 28 zeroes. But when it comes to 125!, we have 5^3 factor so 125!129! have 31 zeroes. So N+2 can be any number between 125 to 129, but the statement also says N1 has 28 zeroes that means N1 can be any number from 120! to 124!. So N can be 125 or 124 or 123 so again Statement 2 is not sufficient. Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer. I got a little doubt Zeros in 120! to 124! is 29 Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29 while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?



Math Expert
Joined: 02 Aug 2009
Posts: 6524

What is the value of N?
[#permalink]
Show Tags
10 Mar 2015, 18:46
ikishan wrote: I got a little doubt
Zeros in 120! to 124! is 29
Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29
while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?
hi, to find power of 5 or zeroes in any factorial, we have to divide the number with increasing power of 5.... 5^1,5^2,5^3 and so on.... you have correctly divided by 5,25 but 75 is wrong as next number would be 5^3=125.. and you cannot divide 120 by 125... so answer is 24+4=28 and not 29... hope it is clear...
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 26 Nov 2014
Posts: 7

Re: What is the value of N?
[#permalink]
Show Tags
11 Mar 2015, 12:09
chetan2u wrote: ikishan wrote: I got a little doubt
Zeros in 120! to 124! is 29
Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29
while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?
hi, to find power of 5 or zeroes in any factorial, we have to divide the number with increasing power of 5.... 5^1,5^2,5^3 and so on.... you have correctly divided by 5,25 but 75 is wrong as next number would be 5^3=125.. and you cannot divide 120 by 125... so answer is 24+4=28 and not 29... hope it is clear... Thanks man, that filled clarity.



NonHuman User
Joined: 09 Sep 2013
Posts: 7716

Re: What is the value of N?
[#permalink]
Show Tags
13 Dec 2017, 05:28
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the value of N? &nbs
[#permalink]
13 Dec 2017, 05:28






