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

Redeem

Interesting GMATFix Problem-16

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Community Manager
Posts: 1048
Joined: Mon Aug 17, 2009 3:26 am
Location: India
Thanked: 51 times
Followed by:27 members
GMAT Score:670

Interesting GMATFix Problem-16

by arora007 » Tue Sep 21, 2010 12:54 pm
x,q and r are positive integers and x/17 =q remainder r.
What is the remainder when x is divided by 34?
1) q is odd
2) r=5
https://www.skiponemeal.org/
https://twitter.com/skiponemeal
Few things are impossible to diligence & skill.Great works are performed not by strength,but by perseverance

pm me if you find junk/spam/abusive language, Lets keep our community clean!!
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Wed Sep 22, 2010 6:46 am
arora007 wrote:x,q and r are positive integers and x/17 =q remainder r.
What is the remainder when x is divided by 34?
1) q is odd
2) r=5
x/17 =q remainder r

1) q is odd
Assume x = 17
q=1,r=0
Reminder of 17/34 = 17
Assume x= 18
q=1,r=1
Reminder of 18/34 = 18
Hence INSUFF

2) r=5
Assume x = 22
q=1, r= 5
Reminder of 17/34 = 17
Assume x = 39
q=2, r= 5
Reminder of 39/34 = 5
hence INSUFF

Combining:
Assume x = 22
q=1, r= 5
Reminder of 22/34 = 22
Assume x = 56
q=3, r= 5
Reminder of = 22
Hence INSUFF

pick C.

Made a Typo. Edited back...
Last edited by kvcpk on Wed Sep 22, 2010 7:28 pm, edited 1 time in total.
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Wed Oct 28, 2009 1:47 pm
Thanked: 1 times

by archiekins2007 » Wed Sep 22, 2010 12:50 pm
The answer is C

If remain = 5 and quotient is odd number as given, according to periodicity of 17 and 34, this information is enough to tell us that the remainder will always be 22.

Regards
Archie
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Fri Sep 03, 2010 11:01 pm
Location: Dubai
Thanked: 2 times

by fatalityish » Wed Sep 22, 2010 1:33 pm
archiekins2007 wrote:The answer is C

If remain = 5 and quotient is odd number as given, according to periodicity of 17 and 34, this information is enough to tell us that the remainder will always be 22.

Regards
Archie
Hey archie your solution is correct. I tried by putting dummy values in the expressions to solve.
Can u please explain what is the periodicity of 17 and 34. I didnt understand what you meant exactly.

Ishaan
Practice makes does a man perfect, but a planned practice takes the man beyond perfection!!!
Top
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Wed Oct 28, 2009 1:47 pm
Thanked: 1 times

by archiekins2007 » Wed Sep 22, 2010 1:43 pm
Hey Ishaan,
Its difficult to put in words but I can try:)
Multiples of 34 will repeat itslef periodically for ever even multiple of 17. So if you draw on a sheet, you will see that if we know that a number divided by 17 has and eve or an odd quientient along with a given remainder, it will always generate the same remainder for 34 as well.
Its kind of like the same approach you used when you put in nunbers, just by drawing it on a number-line.

Regards
Archie
Top
User avatar
Community Manager
Posts: 1048
Joined: Mon Aug 17, 2009 3:26 am
Location: India
Thanked: 51 times
Followed by:27 members
GMAT Score:670

by arora007 » Wed Sep 22, 2010 2:04 pm
OA is C
https://www.skiponemeal.org/
https://twitter.com/skiponemeal
Few things are impossible to diligence & skill.Great works are performed not by strength,but by perseverance

pm me if you find junk/spam/abusive language, Lets keep our community clean!!
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Fri Sep 03, 2010 11:01 pm
Location: Dubai
Thanked: 2 times

by fatalityish » Wed Sep 22, 2010 5:21 pm
archiekins2007 wrote:Hey Ishaan,
Its difficult to put in words but I can try:)
Multiples of 34 will repeat itslef periodically for ever even multiple of 17. So if you draw on a sheet, you will see that if we know that a number divided by 17 has and eve or an odd quientient along with a given remainder, it will always generate the same remainder for 34 as well.
Its kind of like the same approach you used when you put in nunbers, just by drawing it on a number-line.

Regards
Archie
Hey archie,
thanks buddy, i got the idea. since 34 is even multiple of 17 (i.e. 2) the remainder will be the same as that of 17 for all even multiples of 34. And when we divide 34 by odd multiples of 34 we will get the same remainder (22).

I think i will note down this point in my flash cards. Its a very important deduction which can save much time in exam.
Thanks again.
Ishaan
Practice makes does a man perfect, but a planned practice takes the man beyond perfection!!!
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Fri Oct 01, 2010 1:01 pm
using periodicity of a number to determine remainder (r):
please can someone give simpler examples...

Am confused at the explanations given above: e.g
if x/17 = q + r given: x/17 = 1 + r(5)
then for x/34 ==> r = (17 +r )?, where 17 + r = 22, right?
Top
Legendary Member
Posts: 768
Joined: Mon Nov 30, 2009 3:46 am
Thanked: 21 times
Followed by:7 members

by GMATMadeEasy » Sat Oct 02, 2010 2:59 pm
How could be do it algebaricaly ?

That is to set a formula as X = 17q + R and X + 34q1 + r1 ..
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Sun Oct 03, 2010 5:41 am
still don't know how the equation you cited above clarifies my question.
Well, one thing I know is this:
x = 34q + r.....................where x, q, and r are positive integers.
the remainder (r) as above will yield the same value for 17 if
x = 17Q + r only if Q = 2q (even multiple). Also, 17Q <= 34q

likewise for:
x = 68 + R
we expect that for "x = 17(4) + r "
R = r because 68 is an even multiple of 17
Top
Post new topic Post Reply
• Page 1 of 1