If x and y are positive integers, which of the following is NOT a poss

Question

If x and y are positive integers, which of the following is NOT a possible value for  \frac{3*2^x*18^x}{6^{(x+y)}} ?

A.  \frac{1}{12}

B.  \frac{1}{2}

C.  \frac{2}{3}

D. 3

E. 18

andreagonzalez2k · Accepted Answer

\frac{3*2^x*18^x}{6^{(x+y)}}=\frac{3*(2*18)^x}{6^x*6^y}=\frac{3*6^{2x}}{6^x*6^y}=\frac{3*6^x}{6^y}=3*6^{(x-y)}

As x and y are integers, (x-y) can be for example:

-2 -> the expression ends up being  \frac{3}{36}=\frac{1}{12}

-1 -> the expression ends up being  \frac{3}{6}=\frac{1}{2}

0 -> the expression ends up being  3*6^0=3

1 -> the expression ends up being  3*6^1=18

As we see the expression rises as (x-y) rises and decreases as (x-y) decreases.

\frac{2}{3}  is between  \frac{1}{2}  and  3  and the expression never has this value.

IMO C

Papai21 · Answer

Simplifying the given expression we have: 3^(x-y+1) * 2^(1-y)
Comparing this expression with the given answer choices we get values of x and y.
Only for option C. 2/3 
we have the value of x = -2.
But it is given that x and y are positive integers.
Hence option C cannot be true. 
So, IMO ANSWER C

Adarsh_24 · Answer

We will get 
3^(x-y+1) * 2^(x-y)

So power of 3 is 1 greater than power of 2.
If you convert the answer choices into power of 2 and 3.
Only 2/3 won’t follow this rule.

AkshayDang · Answer

Simplify this equation to get 3^(x-y+1) * 2^(1-y)
Match each answer choice to get the answer

DmitryFarberMPrep · Answer

Quick simplification: https://gmatclub.com/forum/download/file.php?id=82832 We're left with three times the ratio of two different powers of 6. The 6 part will give us some new power of 6: positive, negative, or 0. So our solution set looks like this: { .... 3/216, 3/36, 3/6, 3/1, 3*6, 3*36, 3*216, ....} We can verify all the answers that work (e.g. 3/36 = 1/12), or just recognize that we'll never be left with a 2 in the numerator. We might cancel the 3 (as in 1/12 and 1/2), but none of the fractional results will bring new factors to the numerator. GMAT-Club-Forum-ikgvfu31.png

ClaireCHEN · Answer

Eventually we got 3^(x-y+1) as numerator and 2^y as denominator, which means the denominator should be the multiples of 2, therefore answer is C

shubhim20 · Answer

didn't uunderstood the solution after first line  andreagonzalez2k

Bunuel · Answer

The expression simplifies to 3 * 6^(x - y). For example:

If x - y = -2, we get 3 * 1/36.

If x - y = -1, we get 3 * 1/6.

If x - y = 0, we get 3.

If x - y = 1, we get 3 * 6.

If x - y = 2, we get 3 * 6^2

and so on.

As you can see, 2/3 is impossible, as it cannot be written as 3 * 6^n for any integer n.

If x and y are positive integers, which of the following is NOT a poss

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GMAT Problem Solving (PS) Questions

If x and y are positive integers, which of the following is NOT a poss

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