GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jun 2019, 18:08

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

a, b are positive integers. The remainder of a to be divided by 8 is 4

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

Hide Tags

 
Intern
Intern
avatar
B
Joined: 26 Jul 2014
Posts: 11
CAT Tests
a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 09 Nov 2014, 07:21
1
11
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

62% (02:14) correct 38% (02:22) wrong based on 281 sessions

HideShow timer Statistics

a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55670
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 10 Nov 2014, 01:20
1
4
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20


The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

Answer: C.
_________________
Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1793
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 13 Nov 2014, 01:29
5
3
\(\frac{a}{8}\) >>> Remainder = 4

\(\frac{b}{6}\) >>> Remainder = 2

\(\frac{a*b}{8*6}\) >> As numbers & divisors get multiplied, remainder will also get multiplied

Remainder = 4*2 = 8

Answer = V
_________________
Kindly press "+1 Kudos" to appreciate :)
General Discussion
Manager
Manager
avatar
Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 09 Nov 2014, 09:42
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20




Hi Bunuel
Could you please explain the solution?

I got up to this
a=8p+4
b=6q+2

a*b=48pq+16p+24q+8
when a*b is divided by 48,then 48pq is divisible by 48, 16p could be divisible by 48 (16*3) , 24 q could be divisible by 48 (24*2)
so 8 divided by 48 -> Possible reminder 8

Could you please confirm if this is a correct thinking?

Thanks !
Intern
Intern
avatar
B
Joined: 26 Jul 2014
Posts: 11
CAT Tests
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Nov 2014, 07:28
Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20


The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

Answer: C.



I understand the case when a=4 b=2, but what about a=12 b=2, then ab=24. When this 24 is divided by 48, then the remainder is 24.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55670
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Nov 2014, 07:46
h31337u wrote:
Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20


The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

Answer: C.



I understand the case when a=4 b=2, but what about a=12 b=2, then ab=24. When this 24 is divided by 48, then the remainder is 24.


Yes but 24 is not among the options...
_________________
Manager
Manager
avatar
Joined: 03 May 2013
Posts: 67
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Sep 2016, 19:19
Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20


The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

Answer: C.


HI
the series are 4,12,20....44
2,8,14....44
the first number happens to be 44 and the second one is 68, if we divide 68 by 48 we get the reminder 20 which is option E,
i ant denying option A cant be the ans but option E also could be the ans
Current Student
avatar
B
Joined: 24 Jul 2016
Posts: 77
Location: United States (MI)
GMAT 1: 730 Q51 V40
GPA: 3.6
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Sep 2016, 20:16
why will you divide 68 by 48?


Sent from my iPhone using GMAT Club Forum mobile app
Manager
Manager
avatar
Joined: 03 May 2013
Posts: 67
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Sep 2016, 20:50
i misunderstood the stem, thanks for prompt response
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7757
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 12 Sep 2016, 22:38
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20


Hi
Two ways to do it...
a=8x+4..
b=6y+2..

1) convenient way..
Take x and y as 0, and you will get a*b as 4*2=8
C.

2) a*b=(8x+4)(6y+2)=4(2x+1)*2(3y+1)=8(2x+1)(6y+2).....
So a*b is a multiple of 8..
Also the divider is a multiple of 8..
So remainder has to be a multiple of 8..
While doing this , I just thought of this method.
It should work for all cases, I believe.
Only C is a multiple of 8..
C
_________________
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1527
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 06 Sep 2017, 15:38
1
PareshGmat wrote:
\(\frac{a}{8}\) >>> Remainder = 4

\(\frac{b}{6}\) >>> Remainder = 2

\(\frac{a*b}{8*6}\) >> As numbers & divisors get multiplied, remainder will also get multiplied

Remainder = 4*2 = 8

Answer = V



sorry, you are wrong.
you need to erase this post so that other people will not get wrong.
5/3 has remainder 2.
8/7 has remainder 1
but 40 / 21 does not have remainder 2
Manager
Manager
avatar
B
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

Show Tags

New post 02 Nov 2018, 01:47
We can also apply the rule: remainder of a product is the product of remainders

thus in this case:

Rem(ab)--> rem(a) x rem(b) --> 4 x 2 --> 8

where a-->8p+4 and with p as 0, a is 4. and rem(4/48) is 4
same for b

the pitfall for me was that i got stuck with the algebra..which was not needed
GMAT Club Bot
a, b are positive integers. The remainder of a to be divided by 8 is 4   [#permalink] 02 Nov 2018, 01:47
Display posts from previous: Sort by

a, b are positive integers. The remainder of a to be divided by 8 is 4

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


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne