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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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08 Sep 2010, 21:22
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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
[Reveal] Spoiler: OA

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08 Sep 2010, 21:31
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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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22 Sep 2013, 10:13
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?

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

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22 Sep 2013, 11:14
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, 02:29, 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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23 Sep 2013, 01:57
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?

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

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23 Sep 2013, 01:58
Also, can I substitute MGMAT's method to Bunuel's? i.e. does this method apply in general?

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

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23 Sep 2013, 02:18
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.
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]

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13 Apr 2015, 10:34
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]

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16 Apr 2015, 20:09
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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

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

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10 May 2016, 17:45
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]

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19 May 2017, 07:48
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink]

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19 May 2017, 09:25
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?

A. 10
B. 13
C. 18
D. 26
E. 50

$$\frac{a}{b} = \frac{286}{100}$$

Or, $$\frac{a}{b} = \frac{143}{50}$$

Now, $$a = 143 = 13*11$$

So, The divisor of a must be (B) 13
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Re: If a and b are positive integers such that a/b = 2.86, which   [#permalink] 19 May 2017, 09:25
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