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If a and b are positive integers such that a/b=2.86, which

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

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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
[Reveal] Spoiler: OA

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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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 (compilation-of-tips-and-tricks-to-deal-with-remainders-86714.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.
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Re: If a and b are positive integers such that a/b=2.86, which [#permalink]

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

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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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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.
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Re: Reminder question [#permalink]

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

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

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

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

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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:
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Re: Prime Factor [#permalink]

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New post 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?
Re: Prime Factor   [#permalink] 22 Sep 2013, 09:13

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