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The function f(x, y) is defined as the geometric mean of x a

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The function f(x, y) is defined as the geometric mean of x a [#permalink] New post 15 May 2019, 05:23
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The function f(x, y) is defined as the geometric mean of x and y (geometric mean of x and y equals \(\sqrt{xy}\) ), and the function g(x, y) is defined as the least common multiple of x and y. a and b are two different prime numbers.

Quantity A
Quantity B
f(a, b)
g(a, b)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The function f(x, y) is defined as the geometric mean of x a [#permalink] New post 15 May 2019, 13:58
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Carcass wrote:
The function f(x, y) is defined as the geometric mean of x and y (geometric mean of x and y equals \(\sqrt{xy}\) ), and the function g(x, y) is defined as the least common multiple of x and y. a and b are two different prime numbers.

Quantity A
Quantity B
f(a, b)
g(a, b)


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


Let's make some observations about the Least Common Multiple (LCM) of two DIFFERENT PRIME numbers:
The LCM of 2 and 3 is 6
The LCM of 5 and 3 is 15
The LCM of 2 and 7 is 14
The LCM of 5 and 11 is 55
The LCM of 3 and 13 is 39
In general, if a and b are DIFFERENT PRIME numbers, then their LCM = ab


GIVEN: The geometric mean of a and b = √ab

We get:
QUANTITY A: √ab
QUANTITY B: ab

Since ab > 1, we know that ab > √ab

Answer: B

Cheers,
Brent
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Re: The function f(x, y) is defined as the geometric mean of x a   [#permalink] 15 May 2019, 13:58
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