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The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).
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23 Mar 2021, 06:06
23 Mar 2021, 06:06
Expert Reply
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Question Stats:
95% (01:48) correct
4% (01:32) wrong based on 23 sessions
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The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2). What is a + b ?
(A) 0
(B) 3/4
(C) 1
(D) 2
(E) 9/4
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 0
(B) 3/4
(C) 1
(D) 2
(E) 9/4
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).
[#permalink]
23 Mar 2021, 07:13
23 Mar 2021, 07:13
Carcass wrote:
The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2). What is a + b ?
(A) 0
(B) 3/4
(C) 1
(D) 2
(E) 9/4
(A) 0
(B) 3/4
(C) 1
(D) 2
(E) 9/4
We know the point (1, 2) lies ON both lines.
That means the coordinates x = 1 and y = 2 must satisfy both equations.
Take: x = y/4 + a
Replace x and y with 1 and 2 to get: 1 = 2/4 + a
Simplify: 1 = 0.5 + a
Solve: a = 0.5
Take: y = x/4 + b
Replace x and y with 1 and 2 to get: 2 = 1/4 + b
Simplify: 2 = 0.25 + b
Solve: b = 1.75
So, a + b = 0.5 + 1.75 = 2.25 = 9/4
Answer: E
Cheers,
Brent
Re: The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).
[#permalink]
24 Mar 2021, 00:23
24 Mar 2021, 00:23
Since it is given that point (1,2) satisfies both the equations,
I simply added both the equations.
x+y= x/4 +y/4 + a + b
this can be simplified further,
x+y=(x+y)/4 + a + b
which can be written as 3(x+y)/4 = a+b
Now I substituted x=1 and y=2, hence giving the value of a+b as 9/4
Option E is correct
I simply added both the equations.
x+y= x/4 +y/4 + a + b
this can be simplified further,
x+y=(x+y)/4 + a + b
which can be written as 3(x+y)/4 = a+b
Now I substituted x=1 and y=2, hence giving the value of a+b as 9/4
Option E is correct
