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Which of the following is an equation of a line that doe NO [#permalink]
Expert's post 00:00

Question Stats: 46% (00:24) correct 53% (00:47) wrong based on 26 sessions
Which of the following is an equation of a line that doe NOT contain any points in the xy-plane for which both coordinates are integers?

A.$$y=4$$

B. $$y=\frac{1}{2x}$$

C.$$y=x+3$$

D. $$y= x+\frac{1}{2}$$

E. $$y=\frac{1}{2x} + 3$$
[Reveal] Spoiler: OA

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Last edited by chetan2u on 03 Dec 2018, 18:57, edited 1 time in total.
Corrected the OA Director Joined: 20 Apr 2016
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Re: Which of the following is an equation of a line that doe NO [#permalink]
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Carcass wrote:
Which of the following is an equation of a line that doe NOT contain any points in the xy-plane for which both coordinates are integers?

A.$$y=4$$

B. $$y=\frac{1}{2x}$$

C.$$y=x+3$$

D. $$y= x+\frac{1}{2}$$

E. $$y=\frac{1}{2x} + 3$$

[Reveal] Spoiler: OA
OA in 24h

Here looking at the values,

Only option D , which is $$y= x+\frac{1}{2}$$ is not possible because for any integer value of x, y will be fraction
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Re: Which of the following is an equation of a line that doe NO [#permalink]
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How is option E not right? Intern Joined: 15 Sep 2018
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Re: Which of the following is an equation of a line that doe NO [#permalink]
indiragre18 wrote:
How is option E not right? I would also like to know because I did this with 0 and I remembered you can't divide by 0
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Re: Which of the following is an equation of a line that doe NO [#permalink]
Expert's post
Carcass wrote:
Which of the following is an equation of a line that doe NOT contain any points in the xy-plane for which both coordinates are integers?

A.$$y=4$$

B. $$y=\frac{1}{2x}$$

C.$$y=x+3$$

D. $$y= x+\frac{1}{2}$$

E. $$y=\frac{1}{2x} + 3$$

The question or OA is flawed..
A.$$y=4$$.... x could be any integer...both integer possible

B. $$y=\frac{1}{2x}$$.......2xy=1 or xy=$$\frac{1}{2}$$..
If both x and y are integers, xy should be an integer... so both x and y cannot be integers

C.$$y=x+3$$... Possiible

D. $$y= x+\frac{1}{2}$$.......$$y- x=\frac{1}{2}$$..
The difference of two integers cannot be a fraction... so both x and y cannot be integers

E. $$y=\frac{1}{2x} + 3....y-3=\frac{1}{2x}$$........If x is an integer, $$\frac{1}{2x}$$ will be a fraction, then y-3 cannot be a fraction

so answer = B, D, and E

Note - editing the answer accordingly
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: Which of the following is an equation of a line that doe NO [#permalink]
Expert's post
First, know that we have to get an integer for the x coordinate, and an integer for the y coordinate.

for Y = 4, and Y=x+3, we know the obvious answer,

for choice b

y=1/2x ... lets think..

the smallest integer (absolute value-wise) is 0, lets start with that

0=1/2x... nope
y=1/[2(0)].... nope these answers are impossible.

lets try 1

1=1/(2x)

2x=1
then x = 1/2... so that doesn't work

what about..
y=1/2(1)

y=1/2... so no, that wont work.

try a bigger number, like 100

100=1/(2x)
200x=1
x=1/200....

try for x

y=1/[2(100)]
y=1/200.... nope still a fraction and integer pair. no matter what number you put, there will never be integers in both x and y coordinates.

For choice D
plug in any integer

1+1/2= 3/2
1000+ 1/2 = 2001/2.. no matter what you plug in, the number will always end in 1/2. so there will be no integer pairs for the x and y coordinates.

for E

thats just a continuation of B which was 1/(2x)
so, 1/(2x)+3 will always be a fraction, plus the number 3.

we choose B.D,E Re: Which of the following is an equation of a line that doe NO   [#permalink] 12 Feb 2019, 21:23
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