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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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Joined: 02 Sep 2009
Posts: 58396
The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).  [#permalink]

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26 Mar 2019, 05:35
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Difficulty:

35% (medium)

Question Stats:

71% (01:56) correct 29% (02:08) wrong based on 48 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

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Joined: 22 Nov 2018
Posts: 559
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GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).  [#permalink]

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26 Mar 2019, 05:45
By substituting the points in both we arrive at a=.5 b =1.75 so a+b = 2.25 hence option E

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Re: The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).  [#permalink]

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26 Mar 2019, 06:31
Top Contributor
Bunuel 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

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

Cheers,
Brent
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Re: The lines x = y/4 + a and y = x/4 + b intersect at the point (1, 2).   [#permalink] 26 Mar 2019, 06:31
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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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