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Which of the following lines has x-intercept and y-intercept

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by Max@Math Revolution » Thu Aug 04, 2016 3:50 am
Which of the following lines has x-intercept and y-intercept that are integers?
A. y=3x+1
B. y=√x+1
C. y=-2/x
D. y=x^2-1
E. xy=1

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by Brent@GMATPrepNow » Thu Aug 04, 2016 7:15 am
Max@Math Revolution wrote:Which of the following lines has x-intercept and y-intercept that are integers?

A. y= 3x + 1
B. y = √x + 1
C. y = -2/x
D. y = x² - 1
E. xy = 1
IMPORTANT POINT #1: The y-intercept is the point where the x-coordinate is 0
So, let's plug x = 0 into each answer choice.
We get:
A. y= 3(0) + 1 = 1. Integer - KEEP
B. y = √0 + 1 = 1. Integer - KEEP
C. y = -2/0 undefined. ELIMINATE
D. y = 0² - 1 = -1. Integer - KEEP
E. (0)y = 1. When we solve for y, y is undefined. ELIMINATE

We're left with A, B and D
IMPORTANT POINT #2: The x-intercept is the point where the y-coordinate is 0
So, let's plug y = 0 into each answer choice.
We get:
A. 0 = 3x + 1 Solve to get x = -1/3. Not an integer. ELIMINATE
B. 0 = √x + 1 Unsolvable for x. ELIMINATE
D. 0 = x² - 1 x = 1 or -1, Both are integers. KEEP!

Answer: D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Aug 07, 2016 4:50 pm
Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers and the correct answer is D.
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