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If a and b are positive integers such that...

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aramak
 Post subject: If a and b are positive integers such that...
 Post Posted: Thu Jul 14, 2011 4:46 pm 
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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

I had a question on a possible shortcut for solving this problem. Since we know that "b" is not a divisor of "a," would it be feasible to identify 10, 18, 26, and 50 as possible values for "b" (since all of these #s contain either 2's or 5's as prime factors, resulting in a terminating decimal) and therefore conclude that "13" must be a divisor of "a"?
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jnelson0612
 Post subject: Re: If a and b are positive integers such that...
 Post Posted: Sat Jul 30, 2011 9:53 pm 
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aramak 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

I had a question on a possible shortcut for solving this problem. Since we know that "b" is not a divisor of "a," would it be feasible to identify 10, 18, 26, and 50 as possible values for "b" (since all of these #s contain either 2's or 5's as prime factors, resulting in a terminating decimal) and therefore conclude that "13" must be a divisor of "a"?


Hi Aramak,
Let's first discuss what a terminating decimal is. 2.86 is in fact a terminating decimal; 1/3 = .33333333 and so on is a non-terminating decimal.

In addition, "b" can't be 10 because that would make "a" 28.6 which is not an integer.

Here's how I thought about it: 2.86 could be 286/100, so "a" could be 286. I can quickly eliminate answers A and E. I can quickly try to divide 18 into 286 and find that it does not divide in evenly, so eliminate answer C.

I have B and D left. 13 is a factor of 26, so I will only check 26, and it does in fact go in 11 times.

Okay, can I reduce my values? Yes! I could divide each one by 2, and have 143/50=2.86. Okay, now I can get rid of answer D, 26, and choose B, 13.

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Jamie Nelson
ManhattanGMAT Instructor
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hargadonr
 Post subject: Re: If a and b are positive integers such that...
 Post Posted: Tue Jan 17, 2012 5:56 pm 
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Course Students


Posts: 1
there is a method in the book G1 pg 129 that says:

when a is divided by positive integer b result is 4.35 which of the following could be the remainder when A is divided by B?

the method drops the leading 4 and examines the decimal as follows:
35/100 = 7/20 = R/D ; 20R=7D therefore R has 7 as a factor.

if you follow that method for this question you get
86/100 = 43/50 = R/D ; 50R=43D thefor R has 43 as a factor. but this doesn't work. (the answer says R is div by 11,13 and 143)

likewise if you use the 'full number' method in the CAT answer (286/100 = 143/50 = R/D ; 143D=50R therefore D has 11 and 13 as factors) for the book example you don't get the right result:
435/100 = 87/20 = R/D ; 87D=20R D , R has 3 and 29 as factors

can someone explain which method is correct or how you choose between them? thx.
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tim
 Post subject: Re: If a and b are positive integers such that...
 Post Posted: Mon Jan 30, 2012 2:21 am 
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Location: Southwest Airlines, seat 21C
each of these methods is correct for certain types of problems. you have provided two different types of problems here: one where we are interested in a remainder, and the other where we are interested in factors of the numerator. this is the difference between the problems and thus the solution methods..

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Tim Sanders
Manhattan GMAT Instructor
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