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216 = 2^x3^y x and y are integers.

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sandy
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216 = 2^x3^y x and y are integers. [#permalink] New post   25 Aug 2018, 14:55
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\(216 = 2^x3^y\)
x and y are integers.

Quantity A
Quantity B
x
y


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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C
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GreenlightTestPrep
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Re: 216 = 2^x3^y x and y are integers. [#permalink] New post   29 Aug 2018, 07:30
sandy wrote:
\(216 = 2^x3^y\)
x and y are integers.

Quantity A
Quantity B
x
y


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


This questions begs for some prime factorization

216 = (2)(2)(2)(3)(3)(3)
= (2^3)(3^3)

This means: (2^3)(3^3) = (2^x)(3^y)
At this point, we can see that x = 3 and y = 3
In other words, Quantity A = Quantity B

Answer: C

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mariogarciaLA
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Re: 216 = 2^x3^y x and y are integers. [#permalink] New post   23 Feb 2023, 18:20
1
My approach was playing with numbers - I tried seeing if I could get a case where I could make X and Y the same and landed on 3. More lucky than anything else. I will prime factor next time.
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HarishKumar
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Re: 216 = 2^x3^y x and y are integers. [#permalink] New post   05 Mar 2024, 19:54
1
Since 2 and 3 are prime numbers raised to powers and equated to 216, we can be sure that \(2^x3^y\) represent the prime factorization of 216.

216 = 9 x 24

9 = 3 x 3

24 = 6 x 4 => (2 x 3)(2 x 2)

There are three 3s and three 2s

or

\(216 = 2^3 3^3\)

x=3, y=3

BOTH quantities are EQUAL

The answer is C.
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gmatclubot
Re: 216 = 2^x3^y x and y are integers. [#permalink]
05 Mar 2024, 19:54
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