If 2^(x+y)*3^(x-y) = 32/3 then what is the value of product x and y?

Question

If  2^{(x+y)} * 3^{(x-y)} = \frac{32}{3}  then what is the value of product x and y?

A. 2
B. 3
C. 5
D. 6
E. 16

doomedcat · Answer

Thought so the question had a problem, hence removed the solution, sry

Since it is multiplication in the LHS, it becomes easy to equate LHS , RHS

2^(x+y) * 3^(x-y)= 2^5 * 3^-1

equating we get x+y=5 & x-y=-1
solving for x & y , we get 2&3 respt.
hence ans xy = 6

niks18 · Answer

Hi  ggpapas

The question seems to have an error in the highlighted part. It should be multiplication for the answer to be 6. Kindly confirm the source of the question

2^{(x+y)}*3^{(x-y)}=\frac{32}{3}=2^5*3^{-1}

=>x+y=5  &  x-y=-1

therefore,  x=2  &  y=3

Hence  x*y=2*3=6

rahul16singh28 · Answer

Hi  ggpapas ,

Can you please check if the question is correct. I tried for almost 45 minutes to figure out the answer but couldn't get any approach.

saswata4s · Answer

It seems that there is a typo and it should be multiplication instead of addition. Please check once again.

ggpapas · Answer

Hi all,

Yes I had a typo, the addition should be multiply

Thanks!

chetan2u · Answer

2^{x+y}*3^{x-y}=\frac{32}{3}=\frac{2^5}{3}=2^5*3^{-1} ..

So by equating powers
x+y=5 ...
x-y=-1.....x=y-1
So x+y=y-1+y=5.......2y=6....y=3
x=y-1=3-1=2..
xy=3*2=6

D

pushpitkc · Answer

Theory to solve such questions  
The key to solving these kind of problems is to equate the left hand side to the 
right hand side. Once you have a common base on both the side the exponents 
can be equated.

For an equation  Base1^{Exponent1} = Base2^{Exponent2}

If  Base1 = Base2 , then  Exponent1 = Exponent 2

Now, coming back to this question.

2^{(x+y)} * 3^{(x-y)} = \frac{32}{3}  can be re-written as  2^{(x+y)} * 3^{(x-y)} = 2^5 * 3^{-1}

Using this equation we get x+y = 5 and x-y = -1 
Solving for x and y, we get x=2 and y=3 
The product of x and y is  6(Option D)

GSV · Answer

32/3 = 2^5 * 3^ (-1) 
x+y = 5 
x-y = -1 
2x = 4 
x= 2, y =3 
xy = 6

If 2^(x+y)*3^(x-y) = 32/3 then what is the value of product x and y?

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GMAT Problem Solving (PS) Questions

If 2^(x+y)*3^(x-y) = 32/3 then what is the value of product x and y?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards