GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Oct 2018, 11:45

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If d is a positive integer and f is the product of the first

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 478
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post Updated on: 30 Oct 2012, 01:42
15
80
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

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

_________________

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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 28 Jan 2012, 18:18
30
1
28
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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
Re: +ve integer D  [#permalink]

Show Tags

New post 28 Jan 2012, 18:19
4
4
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 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)>n

It'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: everything-about-factorials-on-the-gmat-85592.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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 478
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
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

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 29 Jan 2012, 16:00
enigma123 wrote:
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.


Yes, you take only the integer part. For example how many trailing zeros does 126! have?

126/5+126/5^2+126/5^3=25+5+1=31.

Hope it's clear.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 1
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 04 Jun 2013, 21:17
1
1
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
Intern
avatar
Joined: 22 Feb 2013
Posts: 9
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 04 Jun 2013, 22:25
I'm having trouble understanding "the product of the first 30 positive integers"
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 05 Jun 2013, 00:19
Yahtzeefish wrote:
I'm having trouble understanding "the product of the first 30 positive integers"


The product of the first 30 positive integers = 1*2*3*...*29*30=30!.

Check Factorials chapter of our Math Book for more: everything-about-factorials-on-the-gmat-85592.html

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
S
Joined: 09 Jun 2010
Posts: 945
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 27 Apr 2015, 05:07
1
REALY HARD
just count the numbers of the number 2 and 5, to see that the max is 7.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post Updated on: 28 Apr 2015, 00:29
1
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 discussion

Suppose 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 | Statistics-1 | Statistics-2
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.e-gmat.com


Originally posted by EgmatQuantExpert on 27 Apr 2015, 06:27.
Last edited by EgmatQuantExpert on 28 Apr 2015, 00:29, edited 1 time in total.
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1243
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 28 Apr 2015, 00:17
1
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 discussion

Suppose 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) - anti-debrief ;)

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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 Harley1980

Spot-on analysis and correct answer. Good job done! :-D

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 | Statistics-1 | Statistics-2
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.e-gmat.com

Manager
Manager
User avatar
B
Joined: 21 Jul 2014
Posts: 71
Location: United States
WE: Project Management (Non-Profit and Government)
GMAT ToolKit User Premium Member Reviews Badge
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 01 Jun 2015, 17:10
1
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 discussion

Suppose 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
Intern
avatar
Joined: 03 Jun 2013
Posts: 8
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 30 Dec 2015, 01:07
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 .


From (1) we only know that max possible value of d is 7.

Please re-read the solution: if-d-is-a-positive-integer-and-f-is-the-product-of-the-first-126692.html#p1035835
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6956
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
B
Joined: 30 Jun 2017
Posts: 18
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)
GMAT ToolKit User
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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?
Extra-hard Quant Tests with Brilliant Analytics

Target Test Prep Representative
User avatar
G
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

New post 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 five-two pairs. (Recall that each five-two 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 Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
avatar
B
Joined: 27 Jul 2017
Posts: 51
Re: If d is a positive integer and f is the product of the first  [#permalink]

Show Tags

New post 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!

GMAT Club Bot
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 ] 

Display posts from previous: Sort by

If d is a positive integer and f is the product of the first

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.