Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 May 2010
Posts: 3

If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
Updated on: 03 Oct 2017, 20:26
Question Stats:
53% (01:32) correct 47% (01:30) wrong based on 535 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by xianster on 11 May 2010, 03:32.
Last edited by Bunuel on 03 Oct 2017, 20:26, edited 3 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
11 May 2010, 04:29
xianster wrote: This is a very good post. Thanks! However I was presented with this problem which I cant solve. Anyone can help out using what has been taught?
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
Hope to hear from u guys soon! Thanks! This post was moved from the remainders topic ( compilationoftipsandtrickstodealwithremainders86714.html) to PS subforum as a separate question: \(\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50}\) > \(b=\frac{50a}{143}=\frac{50a}{11*13}\), 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. Answer: B.
_________________




Manager
Joined: 23 Sep 2009
Posts: 89

If a and b are positive integers such that a/b = 2.86, which
[#permalink]
Show Tags
08 Sep 2010, 20:22
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




Intern
Joined: 20 Jan 2010
Posts: 15

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
11 May 2010, 04:35
a/b= 2.86=286/100 = 143/50 a or 143 can have the following divisors  13,11,2
11 , 13 and 2 can be a divisor of 286
Hence option B



Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: Prime Factor
[#permalink]
Show Tags
08 Sep 2010, 20:31
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. Answer: B.
_________________



Manager
Joined: 19 Apr 2010
Posts: 168
Schools: ISB, HEC, Said

If a and b are positive integers such that a/b = 2.86, which
[#permalink]
Show Tags
30 Sep 2010, 00:46
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



Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: Reminder question
[#permalink]
Show Tags
30 Sep 2010, 00:52
prashantbacchewar wrote: If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a?
10 13 18 26 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. Answer: B.
_________________



Senior Manager
Joined: 18 Feb 2008
Posts: 363
Location: Kolkata

Re: Reminder question
[#permalink]
Show Tags
30 Sep 2010, 05:11
Hi Bunuel.Why not D 26.Even it is divisible by 13.Confused b/w b and d?Where am i wrong?Sorry not clear



SVP
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2461
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Reminder question
[#permalink]
Show Tags
30 Sep 2010, 05:26
suyashjhawar wrote: Hi Bunuel.Why not D 26.Even it is divisible by 13.Confused b/w b and d?Where am i wrong?Sorry not clear What if a = 143 and b = 50 a/b = 2.86..do you think 26 divides 143? No. it does not . We have to reduce the fraction to conclude must be true answers. Golden TIP : suppose you are stuck between 13 and 26 , and the question is about the must be true condition. If some integer is divisible by 26, then it is always divisible by 13 > you can not have 2 correct answers, it has to be one of them If some integer is divisible by 13, then it is not always divisible by 26 > unique solution. In such conditions always select the GCF of the numbers, or in simple terms the lowest factor.
_________________
Fight for your dreams : For all those who fear from Verbal lets give it a fightMoney Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership  big benefits and savingsGmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: Reminder question
[#permalink]
Show Tags
30 Sep 2010, 05:31
suyashjhawar wrote: Hi Bunuel.Why not D 26.Even it is divisible by 13.Confused b/w b and d?Where am i wrong?Sorry not clear The question is: "which of the following must be a divisor of \(a\)". We know that \(a\) must be divisible by both 11 and 13, but we don't know whether it's divisible by 2 (in order to be divisible by 2*13=26). Or consider this: \(\frac{a}{b}=\frac{143}{50}\), so the lowest value of \(a\) is 143 and it's not divisible by any of the answer choices but B (13). Hope it's clear.
_________________



Manager
Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
Posts: 125
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37 GMAT 2: 620 Q49 V27 GMAT 3: 700 Q49 V36
WE: Other (Other)

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
17 Oct 2011, 04:12
I did it like this:
We know that a/b =2.86, which means the decimal part i.e. 0.86 = Remainder/Divisor Simplifying the equation, we get Remainder/Divisor = 43/50. So the divisor should be a multiple of 50.Hence answer is E.
Where am I going wrong?



Intern
Joined: 17 Oct 2011
Posts: 3

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
17 Oct 2011, 08:43
GMATmission wrote: I did it like this:
We know that a/b =2.86, which means the decimal part i.e. 0.86 = Remainder/Divisor Simplifying the equation, we get Remainder/Divisor = 43/50. So the divisor should be a multiple of 50.Hence answer is E.
Where am I going wrong? You have to understand the meaning of divisor in this question. Here it just refers to a factor. It asks you the divisor of a (so that remainder becomes zero). If remainder isn't zero, it will be called the divisor for the total division and not just for the dividend. Basically you take divisor as a factor in this question. 50 is the divisor in this division so that the remainder comes as a factor of 43. On second thoughts answer i 50 I'm damn sure. Haha, divisor does refer to b in this case just like GMATmission said. You can crosscheck this way, a,b are integers, so b*2.86 should give an integer. 50 is the answer. Again question should have said 'the divisor' maybe. 'a divisor' is really confusing. But i'd go with 50 if i'veto.



Intern
Joined: 28 Sep 2011
Posts: 43

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
28 Oct 2011, 20:48
From the given answer choices, we can back solve to find that 286 is divisible by 13 and 26. 26 is just a multiple of 13, therefore 13 (which is also a prime) wins.



Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
09 Feb 2012, 13:12
GMATmission wrote: GMATmission wrote: I did it like this:
We know that a/b =2.86, which means the decimal part i.e. 0.86 = Remainder/Divisor Simplifying the equation, we get Remainder/Divisor = 43/50. So the divisor should be a multiple of 50.Hence answer is E.
Where am I going wrong? Can experts please comment on where I am going wrong? You did everything right except that 50 must be a factor of b, which is a divisor in our case, but we are asked about a not b.
_________________



Intern
Joined: 06 Nov 2011
Posts: 34
Location: Germany
Concentration: Entrepreneurship, General Management
GMAT Date: 03102012
GPA: 3

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
07 Mar 2012, 10:19
I solved it with using prime factorization within 20 sec. 286 has primes 2, 11, 13 Maybe it is the wrong or maybe not the best way to solve this.



Manager
Joined: 27 Oct 2011
Posts: 114
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)

Re: If a and b are positive integers such that a/b=2.86, which
[#permalink]
Show Tags
25 Mar 2012, 17:57
Thank you bunuel... That is another way of looking at the question. I looked at it as 50a = 143b. which is almost the same cause you take 50a/143 = b. and 143 is equal to 11*13.



Intern
Joined: 09 Feb 2012
Posts: 43
Location: India
Concentration: Marketing, Strategy
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)

If a and b are positive integers such that a/b = 2.86, which
[#permalink]
Show Tags
Updated on: 27 Apr 2012, 02:01
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
Originally posted by pratikbais on 27 Apr 2012, 01:40.
Last edited by Bunuel on 27 Apr 2012, 02:01, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 61544

Re: If a and b are positive integers such that a/b = 2.86, which
[#permalink]
Show Tags
27 Apr 2012, 02:01
pratikbais wrote: 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 \(\frac{a}{b}=2.86=\frac{286}{100}=\frac{143}{50}\) > \(b=\frac{50a}{143}=\frac{50a}{11*13}\), for \(b\) to be an integer \(a\) must have all the factors of 143 (since 50 has none of them). Hence \(a\) must be divisible by both 11 and 13. Answer: B.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10130
Location: Pune, India

Re: If a and b are positive integers such that a/b = 2.86, which
[#permalink]
Show Tags
27 Apr 2012, 05:11
pratikbais wrote: 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 2.86 = 286/100 = 143/50 = a/b 'a' must be a multiple of 143 (= 11*13) and b must be a multiple of 50. So it 'a' must be divisible by 13. For such questions, check out this post: http://www.veritasprep.com/blog/2011/05 ... emainders/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 26 Feb 2013
Posts: 146

Re: Prime Factor
[#permalink]
Show Tags
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. Answer: B. 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?







Go to page
1 2
Next
[ 40 posts ]



