Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 17:04

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a and b are positive integers, what is the remainder when

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

### Hide Tags

Intern
Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
Followers: 1

Kudos [?]: 107 [7] , given: 1

If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

20 Jul 2013, 09:26
7
KUDOS
24
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

26% (02:31) correct 74% (01:48) wrong based on 665 sessions

### HideShow timer Statistics

If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a.

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

Can post OE if needed.
[Reveal] Spoiler: OA

Last edited by kingflo on 22 Jul 2013, 06:13, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [9] , given: 11628

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

20 Jul 2013, 09:35
9
KUDOS
Expert's post
4
This post was
BOOKMARKED
If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a --> $$b=1.6a$$--> $$b=\frac{8}{5}a$$ --> $$\frac{b}{a}=\frac{8}{5}$$ --> b is a multiple of 8 (8x) and a is a multiple of 5 (5x) --> ab=5x*8x=40x^2. The remainder when $$ab=40x^2$$ is divided by 40 is 0. Sufficient.

(2) Each of a^2 *b and a*b^2 is divisible by 40. If a=2 and b=10, then ab=20 and the the remainder is also 20 but if a=b=40, then ab=40^2 and the remainder si 0. Not sufficient.

_________________
Intern
Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
Followers: 1

Kudos [?]: 107 [0], given: 1

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

20 Jul 2013, 09:39
Could we also pick numbers for (1)?

(1) b = 1,6a
--> pick smart numbers: b=10 , a=16 --> 10*16 / 40 = 4 + R0 --> Sufficient

Right?
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [1] , given: 11628

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

20 Jul 2013, 09:47
1
KUDOS
Expert's post
kingflo wrote:
Could we also pick numbers for (1)?

(1) b = 1,6a
--> pick smart numbers: b=10 , a=16 --> 10*16 / 40 = 4 + R0 --> Sufficient

Right?

This won't work in all cases. If the question were "what is the remainder when ab is divided by 80?", then with your numbers you'd still get that the remainder is 0, and the statement is sufficient. But this would be wrong: if b=5 and a=5, then ab=40 and the remainder is 40 not 0.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15523
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

01 Aug 2014, 01:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15523
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

08 Sep 2015, 09:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 19 Sep 2011
Posts: 22
Followers: 0

Kudos [?]: 2 [0], given: 9

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

08 Sep 2015, 18:37
Hi Bunuel,
i got this question wrong,but can you poiunt out th eflaw in my reasoning here,
what i did was i calculated that b= 8* a /5 and then ab = (8 * a^2 )/5. now if i divide this new ab by 40 i am left with a^2/25. after this i plugged numbers for a and got different remainders i.e if a^2 = 1, 4, 9, 16 etc , i will have different remainders therefore S1 is insufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

08 Sep 2015, 21:37
Jerry1982 wrote:
Hi Bunuel,
i got this question wrong,but can you poiunt out th eflaw in my reasoning here,
what i did was i calculated that b= 8* a /5 and then ab = (8 * a^2 )/5. now if i divide this new ab by 40 i am left with a^2/25. after this i plugged numbers for a and got different remainders i.e if a^2 = 1, 4, 9, 16 etc , i will have different remainders therefore S1 is insufficient.

From b= 8* a /5 (b/a = 8/5) it follows that a must be a multiple of 5, so you should plug only multiples of 5 there.
_________________
Intern
Joined: 14 Mar 2015
Posts: 35
Schools: ISB '18
Followers: 0

Kudos [?]: 7 [3] , given: 11

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

10 Sep 2015, 11:43
3
KUDOS
Bunuel wrote:
kingflo wrote:
Could we also pick numbers for (1)?

(1) b = 1,6a
--> pick smart numbers: b=10 , a=16 --> 10*16 / 40 = 4 + R0 --> Sufficient

Right?

This won't work in all cases. If the question were "what is the remainder when ab is divided by 80?", then with your numbers you'd still get that the remainder is 0, and the statement is sufficient. But this would be wrong: if b=5 and a=5, then ab=40 and the remainder is 40 not 0.

Hope it's clear.

Isn't it possible to actually pick numbers here for (1) ?
We know both 'a' and 'b' have to be positive integers, and b is always 1.6 times of a.
So, all integer combinations which satisfy the condition - b=1.6a can help us.

a --> b = 1.6 a
5 --> 8
10 --> 16
15 --> 24
and likewise, and in all cases remainder will be 0. Right ?
_________________

It ain’t about how hard you hit. It’s about how hard you can get hit and keep moving forward;
how much you can take and keep moving forward.

That’s how winning is done!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15523
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

23 Sep 2016, 02:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 26 Feb 2015
Posts: 27
Concentration: Entrepreneurship, Strategy
GMAT 1: 560 Q46 V19
GMAT 2: 630 Q49 V27
GMAT 3: 680 Q49 V33
GPA: 2.92
WE: Supply Chain Management (Manufacturing)
Followers: 0

Kudos [?]: 0 [0], given: 66

Re: If a and b are positive integers, what is the remainder when [#permalink]

### Show Tags

27 Nov 2016, 10:20
Bunuel wrote:
If a and b are positive integers, what is the remainder when ab is divided by 40?

(1) b is 60% greater than a --> $$b=1.6a$$--> $$b=\frac{8}{5}a$$ --> $$\frac{b}{a}=\frac{8}{5}$$ --> b is a multiple of 8 (8x) and a is a multiple of 5 (5x) --> ab=5x*8x=40x^2. The remainder when $$ab=40x^2$$ is divided by 40 is 0. Sufficient.

(2) Each of a^2 *b and a*b^2 is divisible by 40. If a=2 and b=10, then ab=20 and the the remainder is also 20 but if a=b=40, then ab=40^2 and the remainder si 0. Not sufficient.

In (2), how can I figure out that I should pick 2 and 10
please shed me some light
Re: If a and b are positive integers, what is the remainder when   [#permalink] 27 Nov 2016, 10:20
Similar topics Replies Last post
Similar
Topics:
1 If a and b are positive integers, what is the remainder when 74a+b is 2 24 Mar 2017, 10:07
26 If a and b are positive integers, what is the remainder when 8 27 Jan 2017, 10:38
38 What is the remainder when the positive integer n is divided 20 01 Mar 2017, 11:04
15 What is the remainder when the positive integer x is divided 10 08 Mar 2017, 12:57
8 If x and y are positive integers, what is the remainder when 6 12 Feb 2014, 00:40
Display posts from previous: Sort by

# If a and b are positive integers, what is the remainder when

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.