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# how to solve this! What is the concept!

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Manager
Joined: 28 Jun 2009
Posts: 51
Location: Moscow Russia
how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 07:10
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how to solve this! What is the concept!

$$\frac{1}{x} + \frac{1}{y} = \frac{36}{323}$$
find the value of x-y

(1) x and y are prime.
(2) x>y>1

From the $$\frac{1}{x} + \frac{1}{y} = \frac{36}{323}$$ we get that
x+y=36 and x*y = 323

this comes down to an equation where
-y*y+36y-323=0

where D<0 thus cannot be solved,

Does this mean that OA is E

Artuurs
Intern
Joined: 05 Jun 2009
Posts: 2
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 07:21
1
KUDOS
x+y=36
xy=323

19 and 17 satisfy this condition
but again either of x or y could be 17 hence x-y can be 2 or -2
Manager
Joined: 28 Jun 2009
Posts: 51
Location: Moscow Russia
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 07:24
iwillwin wrote:
x+y=36
xy=323

19 and 17 satisfy this condition
but again either of x or y could be 17 hence x-y can be 2 or -2

Was it guessing or what!

what is the concept being tested
Senior Manager
Joined: 04 Jun 2008
Posts: 286
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 07:25
1
KUDOS
1/x +1/y is same as (x+y)/xy

so we know that xy = 323 or a multiple of it

to find out x and y, factorize 323

You will find that 17*19 = 323
also 17+19 = 36

so we know that x and y are 17 and 19, but not exactly which one is what.

Now look at the options.

For stmt 1: doesnt tell us the values of x and y, insufficient
Stmt 2: tells u that 1<y<x, so you know y=17 and x=19 and both are greater than 1, so no scope for decimals. Sufficient.

ans is B
Senior Manager
Joined: 04 Jun 2008
Posts: 286
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 07:30
1
KUDOS
Note that question doesn't tell us whether x and y are integers or not. So decimals too could satisfy this condition. If it were not given in stmt 2 that x and y are greater than 1, then ans would have been C.
Director
Joined: 01 Apr 2008
Posts: 847
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 12:44
rashminet84 wrote:
Note that question doesn't tell us whether x and y are integers or not. So decimals too could satisfy this condition. If it were not given in stmt 2 that x and y are greater than 1, then ans would have been C.

Didn't get this one..!?
Even if x and y are greater than 1, they can be decimals and can satisfy the proportion.
Director
Joined: 05 Jun 2009
Posts: 731
WE 1: 7years (Financial Services - Consultant, BA)
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 13:01
imo C!

Economist is right!!!

lets say, we just have x>y>1

if we take x as 18.9

then value of Y will be given from

$$1/y = 36/323 - 1/18.9$$

Do you think we can't solve for y. I guess it'll be less than 18.9.
so there are multiple set possible on real number line for this equation.

Need 1 and 2 ==> C
_________________

Consider kudos for the good post ...
My debrief : http://gmatclub.com/forum/journey-670-to-720-q50-v36-long-85083.html

Senior Manager
Joined: 04 Jun 2008
Posts: 286
Re: how to solve this! What is the concept! [#permalink]

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22 Jul 2009, 13:19
sudeep wrote:
imo C!

Economist is right!!!

lets say, we just have x>y>1

if we take x as 18.9

then value of Y will be given from

$$1/y = 36/323 - 1/18.9$$

Do you think we can't solve for y. I guess it'll be less than 18.9.
so there are multiple set possible on real number line for this equation.

Need 1 and 2 ==> C

Yes both of u r right. It should be C.

why didnt i think of decimals greater than 1 when i could think of those less than 1
Re: how to solve this! What is the concept!   [#permalink] 22 Jul 2009, 13:19
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