Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Jul 2013
Posts: 6
Location: United Kingdom
Concentration: Strategy, Finance
GMAT 1: 650 Q42 V38 GMAT 2: 690 Q45 V40
WE: Consulting (Investment Banking)

If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
20 Oct 2013, 07:13
Question Stats:
68% (01:07) correct 32% (01:54) wrong based on 1301 sessions
HideShow timer Statistics
If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ? A) 30 B) 34 C) 36 D) 37 E) 39
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
20 Oct 2013, 07:17




Director
Joined: 03 Feb 2013
Posts: 862
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
20 Oct 2013, 07:18
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 It basically asks for the number of 5s in 150! 150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37 Option d)
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
20 Oct 2013, 07:18



Director
Joined: 09 Jun 2010
Posts: 941

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
30 Apr 2015, 00:28
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 total number of 5 is 150/5=30 among 30 there are 25 50 75 100 125 150 contain 1,1,1,1 ,2 , 1 the number of 5 more total 30+7 d very hard



Manager
Joined: 20 Jan 2017
Posts: 60
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
25 Jan 2017, 09:09
1) To paraphrase the question, we need to find all the prime factors 5 of the number 150! 2) 150/5=30; 150/25=6; 150/125=1. The total number of 5's is 30+6+1=37
Posted from my mobile device



Intern
Joined: 06 Mar 2012
Posts: 16

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
23 Oct 2017, 07:46
Bunuel wrote: This is same as finding trailing zero  right.



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
23 Oct 2017, 07:49



Retired Moderator
Joined: 28 May 2014
Posts: 528

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
23 Oct 2017, 08:11
5^3 < 150 < 5^4 Hence, the total number of 5 in 150!: 150/5^1 + 150/5^2 + 150/5^3 = 30 + 6 + 1 = 37 So, y = 37 Ans: D.
_________________
440 to 730: If I Can, You Can Too



Director
Joined: 13 Mar 2017
Posts: 622
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
23 Oct 2017, 09:32
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 It is asking the number of 5 when the multiplication is written in terms of prime factors So, y = [150/5] + [150/25] + [150/125] = 30 + 6 + 1 = 37 Answer D
_________________
CAT 2017 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Senior SC Moderator
Joined: 22 May 2016
Posts: 2038

If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
23 Oct 2017, 10:55
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 Spelled out a little more: 1) \(x\) = product of integers from 1 to 150 \(x\) = 150 * 149* 148 . . .* 3 * 2 *1: That is, \(x\) = 150! 2) \(5^{y}\) is a factor of 150! What is the greatest possible value of \(y\)? Using \(\frac{150}{5^{y}}\), consider each power \(y\), of 5. Do not worry about remainders. \(\frac{150}{5^1}\) = 30 (5 divides into 150 thirty times) \(\frac{150}{5^2}\) = 6 (25 divides into 150 six times) \(\frac{150}{5^3}\) = 1 (125 divides into 150 only once. Ignore the remainder.) \(5^4 = 625\)  too large to divide into 150 as a factor. 3) Add the results: 30 + 6 + 1 = 37 Answer D Once you know the theory and method, questions such as this one are pretty straightforward. The stats here might indicate that the suggestion below is indispensable. Bunuel wrote: Quote:
_________________
___________________________________________________________________ For what are we born if not to aid one another?  Ernest Hemingway



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
14 Mar 2018, 19:11
Hi All, Since we're multiplying a big string of numbers together, this question comes down to "prime factorization"....we need to "find" all of the 5s that exist in this string of numbers. As a hint, some numbers have MORE THAN one 5 in them. To start, we know that there are 30 multiples of 5 in the string from 1 to 150, so that's 30 5s right there. Now, we need to think about numbers that have more than one 5 in them.... 5, 10, 15....these all have just one 5 25, 50, 75, 100, 150...these all have TWO 5s; we already counted one of the 5s in each, so we have to now add the other one to the total = +5 more 125....this has THREE 5s; we already counted one of the 5s, so we have to now add the other two to the total = +2 more 30 + 5 + 2 = 37 fives. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1267
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
26 Mar 2018, 04:01
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 x is the product of the integers from 1 to 150, inclusive means x = 150! 5^y is a factor of 150! means, \(\frac{150!}{5^y}\) \(= I\), where "I" is an integer We need to calculate the no. of 5s in 150! = \(\frac{150}{5} + \frac{150}{25} + \frac{150}{125}\) = \(30 + 6 + 1\) = \(37\) (D)
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
27 Mar 2018, 11:34
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 The product of the integers from 1 to 150, inclusive, is 150!. To determine the number of factors of 5 within 150!, we can use the following shortcut in which we divide 150 by 5, and then divide the quotient of 150/5 by 5 and continue this process until we can no longer get a nonzero integer as the quotient. 150/5 = 30 30/5 = 6 6/5 = 1 (we can ignore the remainder) Since 1/5 does not produce a nonzero quotient, we can stop. The final step is to add up our quotients; that sum represents the number of factors of 5 within 150!. Thus, there are 30 + 6 + 1 = 37 factors of 5 within 150!. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 27 Jul 2017
Posts: 50

Re: If x is the product of the integers from 1 to 150, inclusive
[#permalink]
Show Tags
03 Apr 2018, 08:35
The answer must be D, i.e. 5 will have a total power of 37 in 150!.
_________________
Ujjwal Sharing is Gaining!




Re: If x is the product of the integers from 1 to 150, inclusive &nbs
[#permalink]
03 Apr 2018, 08:35






