divisor

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kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members; Thanked: 9 times

by kaulnikhil » Fri Sep 25, 2009 3:03 am

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
[spoiler]
why cant we split up 2.86 as 2 +.86 where .86 = quotient/b
and find out which no from the list above is a factor of b [/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri Sep 25, 2009 3:03 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Sep 25, 2009 3:24 am

a/b = 2.86 = 286/100 = 143/50 (in its most simple form), hence a for at least 143 = 11 * 13.

Go with [spoiler]13[/spoiler] in this case.

[spoiler]In this case kaulnikhil, 0.86 â‰ quotient/b, but it is in fact = remainder/b; but even then it won't help you determine about the possible factors of a, as 0.86 is not what we are supposed to look in to.[/spoiler]

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mohitsharda: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Sat Aug 01, 2009 3:13 amFollowed by: 1 member; Thanked: 5 times; GMAT Score:740

Re: divisor

by mohitsharda » Fri Sep 25, 2009 3:49 am

kaulnikhil 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
[spoiler]
why cant we split up 2.86 as 2 +.86 where .86 = quotient/b
and find out which no from the list above is a factor of b [/spoiler]

a/b= 2.86 = 286 / 100 = 143/50
In the question, it says a and b are both integers.
So, b should be a multiple of 50.
=> 143 = 11*13
since, 11 is not in the options, go for 13.

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kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members; Thanked: 9 times

by kaulnikhil » Fri Sep 25, 2009 4:34 am

my mistake ,was finding the divisor of b..

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Pedros: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Thu Mar 26, 2009 3:02 pm; Thanked: 3 times; GMAT Score:410

by Pedros » Fri Sep 25, 2009 6:59 pm

a/b = 2.86

(a * 100 )/b = 286
( a*100)/ 286 = b ( b is an integer )

so a * 100 is divisable by 286 .

prime factors of 100 are { 2,2,5,5 }
Prime factors of 286 are ( 2,13,11}

so a must be divisable by 13.Hence B

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