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 →

a and b are positive integer

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

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] » Tue Oct 07, 2014 10:00 am
Hi j_shreyans,

Before I work through the explanation for this question, you should really put a bit more detail into your posts. Any prompt that involves exponents, multi-variable division, etc. requires details so that the Experts and other users answer the actual question that's asked. If you're going to use carats (the "^" symbol), then you MUST use parentheses to clarify the information. In this prompt, we have unclear information in Fact 2...

When you type a^2b, do you mean....(a^2)(b) or do you mean a^(2b)? These are different math terms and will affect the question in different ways.
The same goes for ab^2....do you mean (a)(b^2) or do you mean (ab)^2?

Since this information is unclear, I'm not going to work through Fact 2. As for the rest of the prompt:

We're told that A and B are POSITIVE INTEGERS. We're asked for the remainder when (A)(B) is divided by 40.

This question is perfect for TESTing VALUES....

Fact 1:B is 60% greater than A

Since both variables must be positive integers, we're really restricted by what we can TEST.

If....
A = 5
B = 8
AB = (5)(8) = 40 and 40/40 = 1r0 so the answer is 0.

A = 10
B = 16
AB = (10)(16) = 160 and 160/40 = 4r0 so the answer is 0.

The answer will ALWAYS = 0 because A MUST be a multiple of 5 and B must be the equivalent multiple of 8. This is the only way for A and B to BOTH be positive integers and for B to be 60% greater than A.
Fact 1 is SUFFICIENT.

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
Master | Next Rank: 500 Posts
Posts: 164
Joined: Sat Sep 20, 2014 10:26 pm
Thanked: 1 times

by jaspreetsra » Tue Oct 07, 2014 5:59 pm
A MUST be a multiple of 5 and B must be the equivalent multiple of 8.Why? didn't get it.
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 Oct 07, 2014 7:04 pm
jaspreetsra wrote:A MUST be a multiple of 5 and B must be the equivalent multiple of 8.Why? didn't get it.
Statement 1: b is 60% greater than a
In other words:
b is 160% of a.

Translated into math:
b = (160/100)a
b/a = 160/100 = 8/5.

Since b and a are INTEGERS in a ratio of 8 to 5, b must be a multiple of 8, while a must be a multiple of 5.
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: 510
Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members
Thanked: 3 times

by j_shreyans » Tue Oct 07, 2014 9:38 pm
[email protected] wrote:Hi j_shreyans,

Before I work through the explanation for this question, you should really put a bit more detail into your posts. Any prompt that involves exponents, multi-variable division, etc. requires details so that the Experts and other users answer the actual question that's asked. If you're going to use carats (the "^" symbol), then you MUST use parentheses to clarify the information. In this prompt, we have unclear information in Fact 2...

When you type a^2b, do you mean....(a^2)(b) or do you mean a^(2b)? These are different math terms and will affect the question in different ways.
The same goes for ab^2....do you mean (a)(b^2) or do you mean (ab)^2?

Since this information is unclear, I'm not going to work through Fact 2. As for the rest of the prompt:

We're told that A and B are POSITIVE INTEGERS. We're asked for the remainder when (A)(B) is divided by 40.

This question is perfect for TESTing VALUES....

Fact 1:B is 60% greater than A

Since both variables must be positive integers, we're really restricted by what we can TEST.

If....
A = 5
B = 8
AB = (5)(8) = 40 and 40/40 = 1r0 so the answer is 0.

A = 10
B = 16
AB = (10)(16) = 160 and 160/40 = 4r0 so the answer is 0.

The answer will ALWAYS = 0 because A MUST be a multiple of 5 and B must be the equivalent multiple of 8. This is the only way for A and B to BOTH be positive integers and for B to be 60% greater than A.
Fact 1 is SUFFICIENT.

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

Well noted , next time i will be more care full.Pls see the below statement 2.

2) Each of (a^2)(b) and (a)(b^2) is divisible by 40

I hope this is clear.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Sun Oct 12, 2014 10:04 pm
Another way to make this legible is to use superscripts. You can copy and paste them from the list given here. Pretty much every instructor except Rich does this, and it makes math much easier to read: to my eyes, (a²b)(b²a) versus a^2bb^2a is kinda of like "Are you doing anything tonight?" vs "r U doin n e thing 2nite??"
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 510
Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members
Thanked: 3 times

by j_shreyans » Thu May 28, 2015 9:18 am
Hi ,

Small doubt in the below question .

Statement 1 says b=160a/100 or 8a/5

so can we put b in the ab/40 then find out the remainder, doing this will get a^2/25 and a is positive integers so by this statement 1 is not sufficient.

Please advise and correct me .

Thanks
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 May 28, 2015 9:32 am
j_shreyans wrote:Hi ,

Small doubt in the below question .

Statement 1 says b=160a/100 or 8a/5

so can we put b in the ab/40 then find out the remainder, doing this will get a^2/25 and a is positive integers so by this statement 1 is not sufficient.

Please advise and correct me .

Thanks
Since b = (8/5)a -- and b is an integer -- a must be a multiple of 5, as in the following cases:
a=5, b = (8/5)(5) = 8.
a=10, b = (8/5)(10) = 16.
a=15, b = (8/5)(15) = 24.
And so on.

Since a is a multiple of 5, a² must be a multiple of 25, implying that dividing a² by 25 will leave a remainder of 0.
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: 518
Joined: Tue May 12, 2015 8:25 pm
Thanked: 10 times

by nikhilgmat31 » Tue Jun 02, 2015 2:12 am
2) Each of (a^2)(b) and (a)(b^2) is divisible by 40

doesn't seems to be sufficient

a*a*b/40

Exp-

Part 1 ==> a= 2 b=10 (a*a*b)/40 2*2*10/40 = 1 is divisible (a*b*b)/40 ==> 2*10*10/40 is divisible OK where as (2*10)/40 is not divisible.

Part 2 ==> a=4 b =10 (a*a*b)/40 4*4*10/40 = 4 OK and (a*b*b)/40 ==> 10*10*4/40 = 10 is divisible where as (4*10)/40 =1 is divisible


B is not sufficient
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1