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 →

For two positive integers A & B, what is the highest num

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 944
Joined: Wed May 30, 2012 8:21 amFollowed by: 5 members
Thanked: 8 times
by RBBmba@2014 » Tue May 12, 2015 3:03 am
For two positive integers A & B, what is the highest number that divides completely the product of integers from 1 to A and 1 to B such that B = A + 29.

(A) 1
(B) Product of all integers from 1 to A
(C) Product of all integers from 1 to B
(D) 29*A
(E) Can't be determined

OA: B

P.S: Interesting question. Although I got this,I'd be looking forward to some better explanation from Experts.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 363
Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members
Thanked: 115 times

by theCEO » Tue May 12, 2015 3:41 am
RBBmba@2014 wrote:For two positive integers A & B, what is the highest number that divides completely the product of integers from 1 to A and 1 to B such that B = A + 29.

(A) 1
(B) Product of all integers from 1 to A
(C) Product of all integers from 1 to B
(D) 29*A
(E) Can't be determined

OA: B

P.S: Interesting question. Although I got this,I'd be looking forward to some better explanation from Experts.
B = A + 29
From this we know that B is greater than A
Therefore B! is greater than A!
B! can be rewritten as i x A! where i is a constant

So the question reads what is the highest number that can divide A! and iA!
A!/A! = 1
iA!/A!= i

Therefore the answer is A! = B
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 » Tue May 12, 2015 5:00 am
RBBmba@2014 wrote:For two positive integers A & B, what is the highest number that divides completely the product of integers from 1 to A and 1 to B such that B = A + 29.

(A) 1
(B) Product of all integers from 1 to A
(C) Product of all integers from 1 to B
(D) 29*A
(E) Can't be determined
The product of the integers from 1 to A = A!.
Since B=A+29, the product of the integers from 1 to B = B! = (A+29)!.

Question stem, rephrased:
What is the greatest common factor of A! and (A+29)!?

Case 1: A=1
Here, A! = 1! and (A+29)! = 30!.
The GCF of 1! and 30! = 1!.

Case 2: A=10
Here, A! = 10! and (A+29)! = 39!.
The GCF of 10! and 39! = 10!.

Case 3: A=100
Here, A! = 100! and (A+29)! = 129!.
The GCF of 100! and 129! = 100!.

In every case, the GCF = A!.

The correct answer is B.
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
Legendary Member
Posts: 944
Joined: Wed May 30, 2012 8:21 amFollowed by: 5 members
Thanked: 8 times

by RBBmba@2014 » Tue May 12, 2015 5:10 am
@ GMATGuru - I did it in the same way (except plugging in numbers), so I believe this is the BEST way to solve this sort of problems! Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue May 12, 2015 7:17 am
RBBmba@2014 wrote:For two positive integers A & B, what is the highest number that divides completely the product of integers from 1 to A and 1 to B such that B = A + 29.

(A) 1
(B) Product of all integers from 1 to A
(C) Product of all integers from 1 to B
(D) 29*A
(E) Can't be determined
NOTE: The question is asking us to find the greatest common factor of A! and B!

Given: B = A + 29

Product of integers from 1 to A = (1)(2)(3)...(A)
Product of integers from 1 to B = (1)(2)(3)...(A)(A+1)(A+2)...(A+28)(A+29)

As you can see, both products SHARE the product (1)(2)(3)...(A), and they share nothing more.
So, (1)(2)(3)...(A) must be the greatest common factor of both products.

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 269
Joined: Sun Apr 27, 2014 10:33 pmFollowed by: 5 members
Thanked: 8 times

by prachi18oct » Wed May 13, 2015 9:56 am
Hello,

I interpreted the question as below :
What is the highest number that divides completely the product of (1 to A) and (1 to B)
I took it in other way :-
highest number that divides completely => (1.2.3.....A)(1.2.3......A+29)
SO it should have been A(A+29).
I think the language of the question is not very clear, atleast to me.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1