Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 478
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
Updated on: 30 Oct 2012, 01:42
Question Stats:
59% (01:23) correct 41% (01:15) wrong based on 1777 sessions
HideShow timer Statistics
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d? (1) 10^d is a factor of f (2) d>6
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Originally posted by enigma123 on 28 Jan 2012, 18:13.
Last edited by Bunuel on 30 Oct 2012, 01:42, edited 2 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 49915

If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
28 Jan 2012, 18:18
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?(1) 10^d is a factor of f > \(k*10^d=30!\). First we should find out how many zeros \(30!\) has, it's called trailing zeros. It can be determined by the power of \(5\) in the number \(30!\) > \(\frac{30}{5}+\frac{30}{25}=6+1=7\) > \(30!\) has \(7\) zeros. \(k*10^d=n*10^7\), (where \(n\) is the product of other multiples of 30!) > it tells us only that max possible value of \(d\) is \(7\). Not sufficient. Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that \(10^d\) is factor of this number, but \(10^d\) can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically \(d\) can be any integer from 1 to 7, inclusive (if \(d>7\) then \(10^d\) won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of \(d\) from this statement. Hence this statement is not sufficient. (2) d>6 Not Sufficient. (1)+(2) From (2) \(d>6\) and from (1) \(d_{max}=7\) > \(d=7\). Answer: C. Hope it 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 Sep 2009
Posts: 49915

Re: +ve integer D
[#permalink]
Show Tags
28 Jan 2012, 18:19
Trailing zeros:Trailing zeros are a sequence of 0s 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 nonnegative 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. For more on this concept check Everything about Factorials on the GMAT: everythingaboutfactorialsonthegmat85592.html
_________________
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



Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 478
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
29 Jan 2012, 15:50
Hi Bunuel thanks  all makes sense apart from the concept of trailing zeros. Am I right in saying this is how you said there will be 7 zero's. 30/5 + 30/25 = 6 + 1 (quotient) = 7. Where I am not clear is have you simply divided 30/25? I hope I am making myself clear, if I am not then please let me know.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
29 Jan 2012, 16:00



Intern
Joined: 02 Apr 2013
Posts: 1

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
04 Jun 2013, 21:17
Hi. I think there is a solution without knowing the trailing zeros formula. Of course I. alone will not be enough (d= 10 or d=100 do the trick) and II. d>6 is vague. Now, to evaluate I and II together, like you know that 10 = 2*5, and 10^x = (2*5)^x = 2^x*5^x, if 10^d is a factor of f, like f = 1*2*3*4*5...*30, you need to see how many 2s and 5ves you can get. You have plenty of 2s, so lets focus on the 5ves. You actually get 7 fives between 1 and 30 (one in 5,10,15,20,30 and two in 25). So basically d could be any number between 1 and 7. Like II is "d>6", you know that d = 7.
(my 1st post, sorry for style... just trying to help, I suck at knowing formulas, although they save you time. (I learned a lot from this forum, Bunuel is my Guru!))



Intern
Joined: 22 Feb 2013
Posts: 9

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
04 Jun 2013, 22:25
I'm having trouble understanding "the product of the first 30 positive integers"



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
05 Jun 2013, 00:19



Director
Joined: 09 Jun 2010
Posts: 945

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
27 Apr 2015, 05:07
REALY HARD just count the numbers of the number 2 and 5, to see that the max is 7.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2063

If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
Updated on: 28 Apr 2015, 00:29
thangvietnam wrote: REALY HARD just count the numbers of the number 2 and 5, to see that the max is 7. I hope the students are clear here about why we only need to consider the number of 5s in the product 30*29*28. . .3*2*1 If not, then please read on. 10 = 2*5 So, to make one 10, we need one 2 and one 5. In the product 30*29*28. . .3*2*1, the number of 2s far exceeds the number of 5s. Therefore, since 5 is the limiting multiplicand here, we only need to consider the number of 5s. Apply this discussionSuppose the question was: If p is the maximum integer such that \(35^p\) is a factor of the product of the first 30 positive integers, what is the value of p?How would you proceed to find the value of p? Regards Japinder
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Retired Moderator
Joined: 06 Jul 2014
Posts: 1243
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
28 Apr 2015, 00:17
EgmatQuantExpert wrote: thangvietnam wrote: REALY HARD just count the numbers of the number 2 and 5, to see that the max is 7. I hope the students are clear here about why we only need to consider the number of 5s in the product 30*29*28. . .3*2*1 If not, then please read on. 10 = 2*5 So, to make one 10, we need one 2 and one 5. In the product 30*29*28. . .3*2*1, the number of 2s far exceeds the number of 5s. Therefore, since 5 is the limiting multiplicand here, we only need to consider the number of 5s. Apply this discussionSuppose the question was: If p is the maximum integer such that \(35^p\) is a factor of the product of the first 30 integers, what is the value of p?How would you proceed to find the value of p? Regards Japinder Hello EgmatQuantExpert. Really artful question ) We know that \(35\) has two factors \(5\) and \(7\) First impulse is to just take answer from previous question because of presence of \(5\) but we should calculate that number, that has less occurrences So \(5\) in \(30!\) meets \(7\) times but \(7\) in \(30!\) meets \(4\) times. And we can infer that \(30!\) will be divisible by \(35\) only \(4\) times. So \(p = 4\)
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2063

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
28 Apr 2015, 04:27
Harley1980 wrote: Hello EgmatQuantExpert. Really artful question ) We know that \(35\) has two factors \(5\) and \(7\) First impulse is to just take answer from previous question because of presence of \(5\) but we should calculate that number, that has less occurrences So \(5\) in \(30!\) meets \(7\) times but \(7\) in \(30!\) meets \(4\) times. And we can infer that \(30!\) will be divisible by \(35\) only \(4\) times. So \(p = 4\) Dear Harley1980Spoton analysis and correct answer. Good job done! Best Regards  Japinder
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Manager
Joined: 21 Jul 2014
Posts: 71
Location: United States
Schools: HBS '16, Stanford '16, Kellogg '16, CBS '16, Ross '17, Haas '16, Haas EWMBA '18, Tuck '17, Stern '18, Yale '17, Anderson '17, Darden '16, Johnson '16, Tepper '18 (D), LBS '17, Insead '14, IMD '16, IE Nov'15, Booth, LBS MiM'17
WE: Project Management (NonProfit and Government)

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
01 Jun 2015, 17:10
EgmatQuantExpert wrote: thangvietnam wrote: REALY HARD just count the numbers of the number 2 and 5, to see that the max is 7. I hope the students are clear here about why we only need to consider the number of 5s in the product 30*29*28. . .3*2*1 If not, then please read on. 10 = 2*5 So, to make one 10, we need one 2 and one 5. In the product 30*29*28. . .3*2*1, the number of 2s far exceeds the number of 5s. Therefore, since 5 is the limiting multiplicand here, we only need to consider the number of 5s. Apply this discussionSuppose the question was: If p is the maximum integer such that \(35^p\) is a factor of the product of the first 30 positive integers, what is the value of p?How would you proceed to find the value of p? Regards Japinder I think We need to do prime factorization of 35 = 5 x 7 so to make one 35 we need one 5 & one 7. Now, we will calculate how many 5's & 7's are there in the 30!. It will be : 30/5 + 30/5x5 = 7 # of 5's Also, 30/7 = 4 # of 7's. Thus, 7 is the limiting multiplicand here. We have four such pairs of 5 x 7 . Thus the maximum power of 35 will be 4 so as to divide 30! evenly. I really like your step by steo approach to each question. Regards, Ankush.



Intern
Joined: 03 Jun 2013
Posts: 8

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
30 Dec 2015, 01:04
Bunuel : I understood the solution but what i didn't understand is ..why isn't statement 1 sufficient. We know the trailing zeros are 7and can only be 7 because it would otherwise exceed 30! ..so wouldn't A be enough to tell us that d=7. although statement 2 says d>6 ..and if we combine them it just reconfirms the same thing. can you pls help me fill the gap in my understanding .



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
30 Dec 2015, 01:07



Math Expert
Joined: 02 Aug 2009
Posts: 6956

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
30 Dec 2015, 01:10
puneetkaur wrote: Bunuel : I understood the solution but what i didn't understand is ..why isn't statement 1 sufficient. We know the trailing zeros are 7and can only be 7 because it would otherwise exceed 30! ..so wouldn't A be enough to tell us that d=7. although statement 2 says d>6 ..and if we combine them it just reconfirms the same thing. can you pls help me fill the gap in my understanding . hi, although asked from bunuel, i'll try it for you.. statement 1 is "(1) 10^d is a factor of f " Also rightly said by you there are 7 0s in 30!.. but 30! factor can be 10^2, 10^1, or 10^7.. we only know tht the max value of d is 7.. hope it helped
_________________
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: 30 Jun 2017
Posts: 18
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
29 Aug 2017, 07:46
Bunuel wrote: If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
(1) 10^d is a factor of f > \(k*10^d=30!\).
First we should find out how many zeros \(30!\) has, it's called trailing zeros. It can be determined by the power of \(5\) in the number \(30!\) > \(\frac{30}{5}+\frac{30}{25}=6+1=7\) > \(30!\) has \(7\) zeros.
\(k*10^d=n*10^7\), (where \(n\) is the product of other multiples of 30!) > it tells us only that max possible value of \(d\) is \(7\). Not sufficient.
Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that \(10^d\) is factor of this number, but \(10^d\) can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically \(d\) can be any integer from 1 to 7, inclusive (if \(d>7\) then \(10^d\) won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of \(d\) from this statement. Hence this statement is not sufficient.
(2) d>6 Not Sufficient.
(1)+(2) From (2) \(d>6\) and from (1) \(d_{max}=7\) > \(d=7\).
Answer: C.
Hope it helps. So the thing is: 10^d is not the only factor, it is one of the factors, that's why we cannot surely say that d=7. But if the question would have said that 10^d is the only factor then, "A" would be the right answer. Am i right?



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
29 Aug 2017, 09:08
saswatdodo wrote: Bunuel wrote: If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
(1) 10^d is a factor of f > \(k*10^d=30!\).
First we should find out how many zeros \(30!\) has, it's called trailing zeros. It can be determined by the power of \(5\) in the number \(30!\) > \(\frac{30}{5}+\frac{30}{25}=6+1=7\) > \(30!\) has \(7\) zeros.
\(k*10^d=n*10^7\), (where \(n\) is the product of other multiples of 30!) > it tells us only that max possible value of \(d\) is \(7\). Not sufficient.
Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that \(10^d\) is factor of this number, but \(10^d\) can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically \(d\) can be any integer from 1 to 7, inclusive (if \(d>7\) then \(10^d\) won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of \(d\) from this statement. Hence this statement is not sufficient.
(2) d>6 Not Sufficient.
(1)+(2) From (2) \(d>6\) and from (1) \(d_{max}=7\) > \(d=7\).
Answer: C.
Hope it helps. So the thing is: 10^d is not the only factor, it is one of the factors, that's why we cannot surely say that d=7. But if the question would have said that 10^d is the only factor then, "A" would be the right answer. Am i right? 1 is the only positive integer which has 1 factor. All other positive integers have more factors. It does not make sense to say that 10^d is the only factor of 30!.
_________________
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
05 Sep 2017, 17:48
enigma123 wrote: If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
(1) 10^d is a factor of f (2) d>6 We are given that d is a positive integer and f = 30!. We need to determine the value of d. Statement One Alone: 10^d is a factor of f Since 10^1 and 10^2 could each divide into 30!, we do not have a unique value for d. Statement one alone is not sufficient to answer the question. Statement Two Alone: d > 6 Since d could be 7, 8, or greater, statement two alone does not allow us to determine a unique value of d. Statements One and Two Together: Using both statements, since we know that d > 6, let’s determine the maximum value d can be given that 10^d divides into 30!. Essentially, we need to determine the maximum number of fivetwo pairs. (Recall that each fivetwo pair creates a factor of 10.) Since there are more twos than fives, let’s determine the number of fives. The factors that are multiples of 5 in 30! are 5, 10, 15, 20, 25 = 5^2, and 30. So, we see there are 7 fives in 30!, and thus the maximum value of d is 7. Since d > 6, d must be 7. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 27 Jul 2017
Posts: 51

Re: If d is a positive integer and f is the product of the first
[#permalink]
Show Tags
05 Apr 2018, 09:10
The answer is C. Statement 1  With the help of statement 1 we can find maximum values of zeros in 30!. Not sufficient. Statement 2  With this, all we know is d>6. Not sufficient. Statement 1 + 2 = # of trailing zeros in 30! is 7 and d>6. So answer is 7. Sufficient.
_________________
Ujjwal Sharing is Gaining!




Re: If d is a positive integer and f is the product of the first &nbs
[#permalink]
05 Apr 2018, 09:10



Go to page
1 2
Next
[ 23 posts ]



