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

 It is currently 23 Jul 2018, 01:12

### 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

# If the fraction 98/(23*89) is written in the form a + b/23 + c/89

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

### Hide Tags

Intern
Joined: 22 Nov 2010
Posts: 2
Location: Lima, Perú
Schools: Owen, Fuqua, Darden, Ross, Geogetown
If the fraction 98/(23*89) is written in the form a + b/23 + c/89  [#permalink]

### Show Tags

22 Nov 2010, 07:09
5
00:00

Difficulty:

75% (hard)

Question Stats:

45% (03:47) correct 55% (04:46) wrong based on 22 sessions

### HideShow timer Statistics

If the fraction 98/(23*89) is written in the form a + b/23 + c/89 , with a,b anc c integer numbers such that:

1<= b < 23
1<= c< 89

Then the sum a + b + c is equal to?

a) 30
b) 31
c) 32
d) 33
e) 34
Retired Moderator
Joined: 02 Sep 2010
Posts: 775
Location: London
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89  [#permalink]

### Show Tags

22 Nov 2010, 22:24
mariellary wrote:
Can anybody help me with this? Is giving me a hard time....

If the fraction 98/(23*89) is written in the form a + b/23 + c/89 , with a,b anc c integer numbers such that:

1<= b < 23
1<= c< 89

Then the sum a + b + c is equal to?

a) 30
b) 31
c) 32
d) 33
e) 34

Thanks a lot!

a+b/23+c/89 = 98/(23*89)
(89*23a+89b+23c)/(23*89) = (98/23*89)

Hence, 89*23a+89b+23c=98
23*(89a+c)=98-89b

We need a b between 1 and 22 such that 98-89b is a multiple of 23
Lets look at the pattern of remainders with 23 that 98-89b leaves for different b :
b=1 ... remainder=9
b=2 ... remainder=12
b=3 ... remainder=15
...
b=5 ... remainder=21
b=6 ... remainder=1
...
b=13 ... remainder=22
b=14 ... remainder=2
...
b=21 ... remainder=0

98-89*21 = -77*23

So b=21 & 89a+c=-77
c=-77-89a
We know c is between 1 and 88, so only valid value of a is -1
with a=-1, c=12

a+b+c=-1+21+12=32

_________________
Intern
Joined: 01 Sep 2010
Posts: 30
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89  [#permalink]

### Show Tags

23 Nov 2010, 01:25
This question is really complicated. Thanks for sharing
Non-Human User
Joined: 09 Sep 2013
Posts: 7335
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89  [#permalink]

### Show Tags

01 Oct 2017, 07:04
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.
_________________
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89 &nbs [#permalink] 01 Oct 2017, 07:04
Display posts from previous: Sort by

# If the fraction 98/(23*89) is written in the form a + b/23 + c/89

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

# Events & Promotions

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