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

Question

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

*An answer will be posted in 2 days.

BrentGMATPrepNow · Answer

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 =  0 ² - 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

MathRevolution · Answer

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.

ameyaprabhu · Answer

Why is B wrong?

B. y=√x+1

when x equals 0 we get y = 1
when y equals 0 we get sqrt x = - 1 ----> x = 1?

so both x and y intercepts are integers.

manhasnoname · Answer

Also, note that \sqrt{x} is never negative on GMAT. so \sqrt{x} is -1 for no value of x.

ameyaprabhu · Answer

you mean to say once we reach the stage of √x = - 1, we should not square both sides at all and discontinue solving?

manhasnoname · Answer

you mean to say once we reach the stage of √x = - 1, we should not square both sides at all and discontinue solving?

Correct!

RichaChampion · Answer

This is a Incorrect question because there are many options given that don't qualify to be a line or line segment.

manhasnoname · Answer

I'd call them all lines but not STRAIGHT LINES.

Is it the case in GMAT that a line implies a straight line?

RichaChampion · Answer

Really? You also call Parabola a Line?
D. y=x^2-1

The Mathematics THAT I have learned so far lines are default straight in nature. I have never Know a Line that is curvical or conical or perhaps spherical.

RichaChampion · Answer

This is the graph of the equation D. y=x^2-1
i.e. a Parabola not a line -
https://www.mathwarehouse.com/quadratic/ ... _graph.gif

This is the graph of XY=1, which is a Hyperbolic Parabola not a line - https://amsi.org.au/ESA_Senior_Years/ima ... /1b_41.png

RichaChampion · Answer

This question is fundamentally wrong. Only Option A is line, rest all 4 options doesn't qualify even to be a line.

MathRevolution · Answer

RichaChampion

We are sorry for typo on the question.
The question should have been

Which of the following lines   or curves   has x-intercept and y-intercept that are integers?

RichaChampion · Answer

In that case also there are two correct answers in one problem solving question.

shivam2506 · Answer

How could a curve be a line? In think either the question is wrong or their is some typo in the question.

The answer IMO is "B"

Ajay09 · Answer

Hi @Bunuel, can you please verify the validity of this question? There are certain options which doesn't even represent an equation of line.

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

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