BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If x is the product of numbers 1 through 150....

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Thu Sep 26, 2013 10:09 am
To find "y" we need power of 5 in 150!
so,
150/5 = 30
30/5 = 6
6/5 = 1
1/5 = 0

Answer = 30 + 6 + 1 = 37
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Thu Sep 26, 2013 11:58 am
Hi fourteenstix,

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: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Sun Jul 08, 2012 12:54 pmFollowed by: 3 members
Thanked: 2 times

by helen.xia@mbawatch » Thu Sep 26, 2013 12:02 pm
The product of 1 to 150 can be written as 150!. To find how many 5's can be divided into 150! I listed all the numbers in the 150! pattern that are divisible by 5:
5, 10, 15, 20.....150

going over those number the first time, there are 30 numbers.

Of those 30 numbers, 25, 50, 75, 100, and 150 are divisible by 5 twice. 125 is divisible by 5 three times.

Therefore: 30 + 5 + 2 = 37.

I guess I don't have the best approach to this problem..can you confirm the answer?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Thu Sep 26, 2013 12:16 pm
x = 150!.
5^y = the number of 5's that can be divided into x.
Count how many times EACH POWER OF 5 can be divided into 150:

150/5¹ = 30.
The calculation above indicates that 150! includes 30 multiples of 5¹.
Each multiple of 5¹ supplies at least one 5.

150/5² = 150/25 = 6.
The calculation above indicates that 150! includes 6 multiples of 5², each of which supplies an additional 5.

150/5³ = 150/125 = 1.
The calculation above indicates that 150! includes one multiple of 5³, supplying one more 5.

Thus, the maximum number of 5's that can be divided into x = 30+6+1 = 37.

The correct answer is D.

A similar problem:
https://www.beatthegmat.com/product-of-t ... 94247.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 40
Joined: Thu Mar 03, 2011 11:27 amFollowed by: 7 members
Location: New Delhi, India
Thanked: 3 times

by rahul.sehgal@btgchampion » Sat Oct 05, 2013 10:08 am
theCodeToGMAT wrote:To find "y" we need power of 5 in 150!
so,
150/5 = 30
30/5 = 6
6/5 = 1
1/5 = 0

Answer = 30 + 6 + 1 = 37

Can you help me understand how you did this ? I mean, why you divide this way ? I might be missing a trick here.
Best Regards,
Rahul Sehgal
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Sat Oct 05, 2013 10:33 am
rahulsehgal wrote:
Can you help me understand how you did this ? I mean, why you divide this way ? I might be missing a trick here.
Refer the Mitch's solution above your post.. the method is exactly the same..
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members
Thanked: 11 times

by gmattesttaker2 » Sun Jun 08, 2014 9:53 pm
[email protected] wrote:Hi fourteenstix,

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: D

GMAT assassins aren't born, they're made,
Rich
Hello Rich,

Thanks for the explanation. Here:
5, 10, 15....these all have just one 5
we have 30 5's.

I have tried to understand this as follows:

For 25, 50, 75, 100, 125, 150 we have one more 5 in each. Hence, we have 6 5's here.

For 125, we have one more 5.

Hence, total = 30 + 6 + 1 = 37

Is this correct?

Thanks a lot for your help.

Best Regards,
Sri
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sun Jun 08, 2014 10:26 pm
Hi Sri,

Yes, your way of organizing this question is correct. One of the "design elements" of most GMAT questions is that they can be solved in a variety of ways (even the "math" can be done in more than one way). This design rewards flexible thinkers; it also means that you won't necessarily get "stuck" if you're not sure how to solve a particular question - there's more than 1 way to the solution, so try to do something.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1