Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 May 2015, 02:21

### 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 such that a/b = 2.86, which

Author Message
TAGS:
Manager
Joined: 23 Sep 2009
Posts: 153
Followers: 1

Kudos [?]: 30 [0], given: 37

If a and b are positive integers such that a/b = 2.86, which [#permalink]  08 Sep 2010, 20:22
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:03) correct 50% (00:57) wrong based on 177 sessions
If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

A. 10
B. 13
C. 18
D. 26
E. 50
[Reveal] Spoiler: OA

_________________

Thanks,
VP

Math Expert
Joined: 02 Sep 2009
Posts: 27505
Followers: 4319

Kudos [?]: 42401 [3] , given: 6024

Re: Prime Factor [#permalink]  08 Sep 2010, 20:31
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
vigneshpandi wrote:
If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

1. 10
2. 13
3. 18
4. 26
5. 50

$$\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50}$$ --> $$b=\frac{50a}{143}=\frac{50a}{11*13}$$, for $$b$$ to be an integer $$a$$ must have all the factors of 143 (50 has none of them). Hence $$a$$ must be divisible by both 11 and 13.

_________________
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 24 [0], given: 25

Re: Prime Factor [#permalink]  22 Sep 2013, 09:13
Bunuel wrote:
vigneshpandi wrote:
If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?

1. 10
2. 13
3. 18
4. 26
5. 50

$$\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50}$$ --> $$b=\frac{50a}{143}=\frac{50a}{11*13}$$, for $$b$$ to be an integer $$a$$ must have all the factors of 143 (50 has none of them). Hence $$a$$ must be divisible by both 11 and 13.

Hi Bunuel,

I'm trying to follow MGMAT's method:
we know that a/b = 2.86
2.86 => 2 and 86/100 or 43/50
and we know that r/b = 43/50
hence 50r = 43b
from that we conclude that b must be a multiple of 50 and 43 a multiple of r.
What am I doing wrong?
Intern
Joined: 18 Aug 2013
Posts: 18
Followers: 0

Kudos [?]: 2 [0], given: 6

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  22 Sep 2013, 10:14
You're doing everything correct. I did the same method, then got stuck near the end as you did. Here's how you would finish the problem.

Since b = 50x, and R = 43x, and a/b = 2 + R/b

a = 2b + R.

So a is equal to 143 (x = 1), 283 (x = 2), etc... In each of these, a is a multiple of 11 and 13.

Looking back, Bunuel's method is method is much easier, as it ignores calculations involving the remainder.

Last edited by grant1377 on 23 Sep 2013, 01:29, edited 1 time in total.
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 24 [0], given: 25

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  23 Sep 2013, 00:57
grant1377 wrote:
You're doing everything correct. I did the same method, then got suck near the end as you did. Here's how you would finish the problem.

Since b = 50x, and R = 43x, and a/b = 2 + R/b

a = 2b + R.

So a is equal to 143 (x = 1), 283 (x = 2), etc... In each of these, a is a multiple of 11 and 13.

Looking back, Bunuel's method is method is much easier, as it ignores calculations involving the remainder.

Hi mate, thanks for the reply. I got a question.
if x = 1, then 50x would be 50 and 43x would be 43, hence 93.
Can you explain in more detail please?
Manager
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 24 [0], given: 25

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  23 Sep 2013, 00:58
Also, can I substitute MGMAT's method to Bunuel's? i.e. does this method apply in general?
Math Expert
Joined: 02 Sep 2009
Posts: 27505
Followers: 4319

Kudos [?]: 42401 [0], given: 6024

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  23 Sep 2013, 01:18
Expert's post
Skag55 wrote:
grant1377 wrote:
You're doing everything correct. I did the same method, then got suck near the end as you did. Here's how you would finish the problem.

Since b = 50x, and R = 43x, and a/b = 2 + R/b

a = 2b + R.

So a is equal to 143 (x = 1), 283 (x = 2), etc... In each of these, a is a multiple of 11 and 13.

Looking back, Bunuel's method is method is much easier, as it ignores calculations involving the remainder.

Hi mate, thanks for the reply. I got a question.
if x = 1, then 50x would be 50 and 43x would be 43, hence 93.
Can you explain in more detail please?

It's 2B, not B --> A = 2B + R = 2*50x + 43x = 143x.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4943
Followers: 299

Kudos [?]: 55 [0], given: 0

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  13 Apr 2015, 09:34
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 2201
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 95

Kudos [?]: 594 [1] , given: 42

Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]  16 Apr 2015, 19:09
1
KUDOS
Expert's post
Hi All,

The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86

We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).

The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86

These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...

A = 143
B = 50
143/50 = 2.86

There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....

Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts

Re: If a and b are positive integers such that a/b = 2.86, which   [#permalink] 16 Apr 2015, 19:09
Similar topics Replies Last post
Similar
Topics:
4 If a and b are positive integers such that a/b = 2.86, which 4 27 Apr 2012, 01:40
8 If a and b are positive integers such that a/b = 2.86, which 8 30 Sep 2010, 00:46
19 If a and b are positive integers such that a/b=2.86, which 17 11 May 2010, 03:32
If a and b are positive integers such that a-b and a/b are 5 26 Jul 2007, 13:38
If a and b are positive integers such that a-b and a/b 6 04 Jul 2005, 02:34
Display posts from previous: Sort by