GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The function f(x, y) is defined as the geometric mean of x a
[#permalink]
15 May 2019, 05:23
15 May 2019, 05:23
Expert Reply
4
Bookmarks
00:00
Question Stats:
70% (01:01) correct
29% (00:57) wrong based on 109 sessions
Hide Show timer Statistics
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
[#permalink]
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
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
[#permalink]
03 Jul 2021, 04:47
03 Jul 2021, 04:47
2
1
Bookmarks
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
