smallest number

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 am; Thanked: 17 times; Followed by:1 members

smallest number

by rahul.s » Mon Jan 25, 2010 11:24 pm

Which of the following is the smallest number?

OA: E

I'd like to learn some approaches to tackle this problem. I spent a good 5 minutes calculating!

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Source: Beat The GMAT — Problem Solving | Mon Jan 25, 2010 11:24 pm

ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pm; Thanked: 26 times; Followed by:1 members

by ace_gre » Mon Jan 25, 2010 11:35 pm

My approach would be to resolve the fractions into prime factors. In this case whichever number has the largest denominator is the smallest number.

After resolving into prime factors cancel out the common terms ...

A) 3^2 * 5^6 * 2^2

B) 2 ^4 * 5^7

C) 5^7 * 2^3

D) 2^2 * 5^7

E) 3 * 2^4 *5^6

Then cancelling 5^6 and 2^2 in all the terms..
We know right away D and E are smaller than B.
Then between B and A, B is greater.
Then evaluate B and E. E is greater of all. Hence 1/E will be the smallest fraction.

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Tue Jan 26, 2010 1:41 am

rahul.s wrote:Which of the following is the smallest number?

OA: E

I'd like to learn some approaches to tackle this problem. I spent a good 5 minutes calculating!

arrange the denomn in terms of (5^5)*x

1/5^5*180
1/5^5*80
1/5^5*200
1/5^5*100
1/5^5*240

clearly E is smallest

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 am; Thanked: 20 times; Followed by:1 members

by bhumika.k.shah » Tue Jan 26, 2010 6:19 am

could you please elaborate???

thephoenix wrote:
rahul.s wrote:Which of the following is the smallest number?

OA: E

I'd like to learn some approaches to tackle this problem. I spent a good 5 minutes calculating!
arrange the denomn in terms of (5^5)*x

1/5^5*180
1/5^5*80
1/5^5*200
1/5^5*100
1/5^5*240

clearly E is smallest

Quote

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Tue Jan 26, 2010 6:27 am

bhumika.k.shah wrote:could you please elaborate???

thephoenix wrote:
rahul.s wrote:Which of the following is the smallest number?

OA: E

I'd like to learn some approaches to tackle this problem. I spent a good 5 minutes calculating!
arrange the denomn in terms of (5^5)*x

1/5^5*180
1/5^5*80
1/5^5*200
1/5^5*100
1/5^5*240

clearly E is smallest

a)1/900*5^4=1/180*5^5
b)1/80*5^5
c)1/5000*5^3=1/1000*5^4=1/200*5^5
likewise converting everything in terms of 5^5
d)2/40*5^5=2/200*5^5=1/100*5^5
e)1/30000*5^2=1/6000*5^3=1/1200*5^4=1/240*5^5

now each deno is in the form 5^5 * x so it depends on x the larger the x the smaller the no. is which is E