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If x and y are positive integers,what is the value of x + y?
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Author:  A4G [ 03 Dec 2013, 16:09 ]
Post subject:  If x and y are positive integers,what is the value of x + y?

If x and y are positive integers, what is the value of x + y ?


(1) \(2^x 3^y= 72\)

(2) \(2^x 2^y = 32\)

Author:  A4G [ 03 Dec 2013, 16:13 ]
Post subject:  Re: If x and y are positive integers,what is the value of x + y?

A4G wrote:
If x and y are positive integers, what is the value of x + y ?
(1) 2^x 3^y= 72
(2) 2^x 2^y = 32


Statement 1:
Since x and y are integers, there is only possibility.
72 = 8*9 = 2^3 * 3^2
So x = 3 and y = 2.
We can find x+y = 3+2 = 5 =>Sufficient .

Statement 2 :
LHS : 2^x 2^y = 2^(x+y)
RHS : 32 = 2^5
2^(x+y) = 2^5
Hence x+y = 5. =>Sufficient .

Answer = D

Author:  Kinshook [ 21 Jul 2019, 03:33 ]
Post subject:  Re: If x and y are positive integers,what is the value of x + y?

A4G wrote:
If x and y are positive integers, what is the value of x + y ?


(1) \(2^x 3^y= 72\)

(2) \(2^x 2^y = 32\)



Given: x and y are positive integers
Asked: What is the value of x + y ?

(1) \(2^x 3^y= 72\)
\(2^x 3^y= 72 = 2^3*3^2\)
x=3 y=2
x+y = 5
SUFFICIENT


(2) \(2^x 2^y = 32\)[/quote]
\(2^x 2^y = 32\) = 2^5
x+y = 5
SUFFICIENT

IMO D

Author:  bumpbot [ 25 Jan 2022, 09:37 ]
Post subject:  Re: x and y are positive not positive integers

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