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If a and b are positive integers such that a/b=2.86, which [#permalink]
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11 May 2010, 03:32
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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
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Last edited by Bunuel on 03 Oct 2017, 20:26, edited 3 times in total.
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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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11 May 2010, 04:29
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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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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



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If a and b are positive integers such that a/b = 2.86, which [#permalink]
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08 Sep 2010, 20:22
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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
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Re: Prime Factor [#permalink]
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08 Sep 2010, 20:31
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If a and b are positive integers such that a/b = 2.86, which [#permalink]
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30 Sep 2010, 00:46
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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



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Re: Reminder question [#permalink]
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30 Sep 2010, 00:52
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Re: Reminder question [#permalink]
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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



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Re: Reminder question [#permalink]
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30 Sep 2010, 05:26
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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.
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Re: Reminder question [#permalink]
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30 Sep 2010, 05:31



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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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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?
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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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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.



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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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28 Oct 2011, 20:48
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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.



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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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09 Feb 2012, 13:12



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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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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.



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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]
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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.
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If a and b are positive integers such that a/b = 2.86, which [#permalink]
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27 Apr 2012, 01:40
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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
Last edited by Bunuel on 27 Apr 2012, 02:01, edited 1 time in total.
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]
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27 Apr 2012, 02:01
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]
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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/
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Re: Prime Factor [#permalink]
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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?







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