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Intern  Joined: 06 May 2010
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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

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 V
Joined: 02 Sep 2009
Posts: 61544
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.

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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
##### General Discussion
Intern  Joined: 20 Jan 2010
Posts: 15
Re: If a and b are positive integers such that a/b=2.86, which  [#permalink]

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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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Joined: 02 Sep 2009
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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.

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 61544

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1
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.

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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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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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Math Expert V
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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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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]

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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.
Intern  Joined: 28 Sep 2011
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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.
Math Expert V
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Posts: 61544
Re: If a and b are positive integers such that a/b=2.86, which  [#permalink]

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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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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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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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4
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 V
Joined: 02 Sep 2009
Posts: 61544
Re: If a and b are positive integers such that a/b = 2.86, which  [#permalink]

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1
1
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.

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Posts: 10130
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Re: If a and b are positive integers such that a/b = 2.86, which  [#permalink]

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1
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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Manager  Joined: 26 Feb 2013
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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? Re: Prime Factor   [#permalink] 22 Sep 2013, 09:13

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