If x y 0, does 3^(x + 1) + 3(2^y) = 12v?

Question

If  x > y > 0 , does  3^{x + 1}  +  3(2^y)  =  12v ?

(1)  \frac{(3^{2x} - 2^{2y})}{(3^{x} - 2^{y})}  =  4v

(2)  2(3^{x+2}) + 9(2^{y+1})  =  72v

ccooley · Accepted Answer

This is a little more complex than most algebra DS problems I've seen.

That said, since it has algebra in it, my first thought is to simplify both the question and the statements as much as possible.

The  3^{x + 1}  in the question, along with the other 3 in the question, makes me think about factoring out a 3 term. That would get rid of the 'x + 1' and make things look simpler, so let's do it.

does  3^{x + 1}  +  3(2^y)  =  12v ?
does  3(3^{x} + 2^{y}) = 12v ?
does  3^{x} + 2^{y} = 4v ?

Much nicer.

Now, go to the statements.

Statement 1 :  \frac{(3^{2x} - 2^{2y})}{(3^{x} - 2^{y})}  =  4v

What I noticed is that both of the values on the top of the fraction are perfect squares. I know that because both of the exponents are even (they both have 2s in the exponents.) I know a rule about the difference of perfect squares - here's the rule:

a^2 - b^2 = (a + b)(a - b)

Let's rewrite the top of the fraction as a difference of squares, then simplify it like that.

(3^{2x} - 2^{2y}) 
 (3^{x})^2 - (2^{y})^2 
 (3^{x} - 2^{y})(3^{x}+2^{y})

Now, there's a common term in the top and bottom of the fraction. Divide it out of both the top and the bottom:

\frac{(3^{x} - 2^{y})(3^{x}+2^{y})}{(3^{x} - 2^{y})} 
  3^{x}+2^{y}

The whole statement simplifies like this:

3^{x}+2^{y} = 4v

That's our question exactly, so it's sufficient.

Statement 2 : This statement looks similar to the question, but it's not exactly the same. I want to get rid of the 'x + 2' and the 'y + 1', since I don't have those in the original question. To turn the x + 2 exponent into an x, like in the question, I need to factor out  3^2  To turn the y + 1 into a y, I need to factor out a 2. Here's how it looks:

2(3^{x+2}) + 9(2^{y+1})  =  72v 
 2*3^2*(3^{x}) + 9*2*(2^{y})  =  72v 
 18(3^{x}) + 18(2^{y})  =  72v

Divide both sides by 18...

3^{x} + 2^{y} = 4v

Again, that's our question, so this statement is sufficient as well.

vangramz · Answer

The question seems incorrect in that we don't even need the two options The LHS is clearly an even + odd which will always be odd and the RHS is even since its a multiple of 2.

avikalagarwal · Answer

The question doesn't state that x and y are integers. Hence, we can't assume that 3^x = even and 2^y = odd.

If x > y > 0, does 3^(x + 1) + 3(2^y) = 12v?

Prep Toolkit

Top 5 GMAT Debrief Videos

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

GMAT Data Sufficiency (DS) Questions