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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] New post 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
[Reveal] Spoiler: OA

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Re: Prime Factor [#permalink] New post 08 Sep 2010, 20:31
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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.

Answer: B.
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Re: Prime Factor [#permalink] 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?
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Re: If a and b are positive integers such that a/b = 2.86, which [#permalink] New post 22 Sep 2013, 10:14
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, 01:29, 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] New post 23 Sep 2013, 00:57
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] New post 23 Sep 2013, 00:58
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] New post 23 Sep 2013, 01:18
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If a and b are positive integers such that a/b = 2.86, which   [#permalink] 23 Sep 2013, 01:18
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