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The function f(x, y) is defined as the geometric mean of x a
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15 May 2019, 05:23
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.
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.
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The function f(x, y) is defined as the geometric mean of x a
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15 May 2019, 13:58
15 May 2019, 13:58
2
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.
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.
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
Retired Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: The function f(x, y) is defined as the geometric mean of x a
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03 Jul 2021, 04:47
03 Jul 2021, 04:47
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Quantity A: f(a, b)
f(x, y) is defined as the geometric mean of x and y (geometric mean of x and y equals \(\sqrt{xy}\) )
=> f(a,b) = \(\sqrt{ab}\)
Quantity B: g(a, b)
g(x, y) is defined as the least common multiple of x and y
=> g(a,b) = LCM(a,b)
Now, we know that a and b are two different prime numbers
And LCM(a,b) = a*b if a and b are co-prime numbers. [Since a and b are prime numbers so they will be co-prime too, that means they have only 1 as the common factor]
=> g(a,b) = ab
Clearly, Quantity A ( \(\sqrt{ab}\) ) < Quantity B (ab)
So, answer will be B
Hope it helps!
To learn more about Functions watch the following video
f(x, y) is defined as the geometric mean of x and y (geometric mean of x and y equals \(\sqrt{xy}\) )
=> f(a,b) = \(\sqrt{ab}\)
Quantity B: g(a, b)
g(x, y) is defined as the least common multiple of x and y
=> g(a,b) = LCM(a,b)
Now, we know that a and b are two different prime numbers
And LCM(a,b) = a*b if a and b are co-prime numbers. [Since a and b are prime numbers so they will be co-prime too, that means they have only 1 as the common factor]
=> g(a,b) = ab
Clearly, Quantity A ( \(\sqrt{ab}\) ) < Quantity B (ab)
So, answer will be B
Hope it helps!
To learn more about Functions watch the following video
