GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 Jan 2020, 15:06

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

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

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60727
If the fraction 98/(23*89) is written in the form a + b/23 + c/89, wil  [#permalink]

Show Tags

New post 05 Dec 2019, 01:37
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

24% (01:44) correct 76% (03:01) wrong based on 17 sessions

HideShow timer Statistics

If the fraction \(\frac{98}{23*89}\) is written in the form \(a + \frac{b}{23} + \frac{c}{89}\), with a, b and c are integers such that:

\(1 \leq b < 23\)
\(1 \leq c< 89\)

Then the sum \(a + b + c\) is equal to?

A. 30
B. 31
C. 32
D. 33
E. 34


Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8327
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89, wil  [#permalink]

Show Tags

New post 05 Dec 2019, 06:06
2
Bunuel wrote:
If the fraction \(\frac{98}{23*89}\) is written in the form \(a + \frac{b}{23} + \frac{c}{89}\), with a, b and c are integers such that:

\(1 \leq b < 23\)
\(1 \leq c< 89\)

Then the sum \(a + b + c\) is equal to?

A. 30
B. 31
C. 32
D. 33
E. 34


Are You Up For the Challenge: 700 Level Questions


\(a + \frac{b}{23} + \frac{c}{89}=\)\(\frac{98}{23*89}\)..
So, now \(\frac{98}{23*89}\)<1, so a will surely not be >1.
Can it be 0? If a=0, then \(0 + \frac{b}{23} + \frac{c}{89}=\)\(\frac{98}{23*89}...89b+23c=98\).... b and c are at least 1, so a cannot be 0.
Can it be -1? If a is -2, then (-2)+(0 to 1)+(0 to 1)=(-2)+(0 to 2) = -something. Thus a can only be -1

Now \(a + \frac{b}{23} + \frac{c}{89}=\)\(\frac{98}{23*89}....23*89a+89b+23c=98....89b+23c=98+23*89=9+89+23*89=9+24*89\)..
\(24*89-b*89=23c-9.....89(24-b)=23c-9\)
Now, 89 is a prime number, so 23c-9 has to be a multiple of 89...23c-9=89x
when x=1...23c-9=89...23c=98...c is NOT an integer
when x=2...23c-9=89*2...23c=198+9...c is NOT an integer
when x=3...23c-9=89*3...23c=267+9=276...c =12
so 24-b=x=3...b=21

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

C
_________________
GMAT Club Bot
Re: If the fraction 98/(23*89) is written in the form a + b/23 + c/89, wil   [#permalink] 05 Dec 2019, 06:06
Display posts from previous: Sort by

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

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





cron

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