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The functions f and g are defined as f(x, y) = 2x + y and g
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14 May 2019, 01:12
14 May 2019, 01:12
Expert Reply
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The functions f and g are defined as f(x, y) = 2x + y and g(x, y) = x + 2y.
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(3, 4) + g(3, 4) |
f(4, 3) + g(4, 3) |
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.
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Joined: 13 May 2019
Affiliations: Partner at MyGuru LLC.
Posts: 186
Given Kudos: 5
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE:Education (Education)
Re: The functions f and g are defined as f(x, y) = 2x + y and g
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14 May 2019, 08:15
14 May 2019, 08:15
Expert Reply
When provided algebra for Quantitative Comparison problems, consider solving algebraically first, because the approach is likely to be more efficient than plugging in.
In this case we have:
Now, in the root statement f(x, y) = 2x + y and g(x + y) = x + 2y | Since both quantities sum these equations, stack and sum the full equations to efficiently compare the quantities.
2x + y
+ x + 2y
3x + 3y
Without plugging in, it can be determined that when adding the two functions of both quantities the x and y coefficients will remain equal. Therefore, since the x and y values are the same in both quantities, the quantities themselves will always be equal, which is choice C.
In this case we have:
Quantity A |
Quantity B |
f(3, 4) + g(3, 4) |
f(4, 3) + g(4, 3) |
Now, in the root statement f(x, y) = 2x + y and g(x + y) = x + 2y | Since both quantities sum these equations, stack and sum the full equations to efficiently compare the quantities.
2x + y
+ x + 2y
3x + 3y
Without plugging in, it can be determined that when adding the two functions of both quantities the x and y coefficients will remain equal. Therefore, since the x and y values are the same in both quantities, the quantities themselves will always be equal, which is choice C.
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
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 functions f and g are defined as f(x, y) = 2x + y and g
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11 Dec 2021, 09:05
11 Dec 2021, 09:05
1
Given that f(x, y) = 2x + y and g(x, y) = x + 2y and we need to find the values for Quantity A and Quantity B
Quantity A = f(3, 4) + g(3, 4)
To find value of of f(3,4) we need to replace x, y with 3, 4 in f(x, y)
=> f(3, 4) = 2*3 + 4 = 6 + 4 = 10
To find value of of g(3,4) we need to replace x, y with 3, 4 in g(x, y)
=> g(3, 4) = 3 + 2*4 = 3 + 8 = 11
=> f(3, 4) + g(3, 4) = 10 + 11 = 21
Quantity B = f(4, 3) + g(4, 3)
To find value of of f(4,3) we need to replace x, y with 4, 3 in f(x, y)
=> f(4, 3) = 2*4 + 3 = 8 + 3 = 11
To find value of of g(4,3) we need to replace x, y with 4, 3 in g(x, y)
=> g(4, 3) = 4 + 2*3 = 4 + 6 = 10
=> f(4, 3) + g(4, 3) = 11 + 10 = 21
Clearly, Quantity A (21) = Quantity B (21)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
Quantity A = f(3, 4) + g(3, 4)
To find value of of f(3,4) we need to replace x, y with 3, 4 in f(x, y)
=> f(3, 4) = 2*3 + 4 = 6 + 4 = 10
To find value of of g(3,4) we need to replace x, y with 3, 4 in g(x, y)
=> g(3, 4) = 3 + 2*4 = 3 + 8 = 11
=> f(3, 4) + g(3, 4) = 10 + 11 = 21
Quantity B = f(4, 3) + g(4, 3)
To find value of of f(4,3) we need to replace x, y with 4, 3 in f(x, y)
=> f(4, 3) = 2*4 + 3 = 8 + 3 = 11
To find value of of g(4,3) we need to replace x, y with 4, 3 in g(x, y)
=> g(4, 3) = 4 + 2*3 = 4 + 6 = 10
=> f(4, 3) + g(4, 3) = 11 + 10 = 21
Clearly, Quantity A (21) = Quantity B (21)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
