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Which of the following is an equation of a line that doe NO
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Updated on: 03 Dec 2018, 18:57

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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. \(y=\frac{1}{2x} + 3\)

_________________

A.\(y=4\)

B. \(y=\frac{1}{2x}\)

C.\(y=x+3\)

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

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

_________________

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Re: Which of the following is an equation of a line that doe NO
[#permalink]
06 Dec 2017, 07:57

1

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. \(y=\frac{1}{2x} + 3\)

A.\(y=4\)

B. \(y=\frac{1}{2x}\)

C.\(y=x+3\)

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

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

Show: :: 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]
02 Nov 2018, 11:32

1

How is option E not right?

Re: Which of the following is an equation of a line that doe NO
[#permalink]
03 Dec 2018, 13:14

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

Re: Which of the following is an equation of a line that doe NO
[#permalink]
03 Dec 2018, 18:56

1

Expert Reply

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. \(y=\frac{1}{2x} + 3\)

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

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

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

1

Expert Reply

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

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
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24 Oct 2021, 08:35

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