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Which of the following lines in the xy-plane does not contai

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5

Problem Solving
Question: 83
Category: Algebra; Arithmetic Substitution; Operations with rationa l numbers
Page: 72
Difficulty: 600


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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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SOLUTION

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5

The answer is y=x+1/2, since for any integer value of x, y becomes integer and a half: .

Answer: B.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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(B) y = x + 1/2 -> for integer values of x, y is not an integer. If x = 1/2, 3/2 etc (non-integers), y is an integer. x and y cannot both be integers.
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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(A) y = x: Solving for x & y intercepts, we get (0, 0) Integer
(B) y = x + 1/2: Solving for x & y intercepts, we get (-1/2, 1/2) Non-Integer (Correct)
(C) y = x + 5: Solving for x & y intercepts, we get (-5, 5) Integer
(D) y = x*1/2: Solving for x & y intercepts, we get (0, 0) Integer
(E) y = x/2 + 5: Solving for x & y intercepts, we get (-10, 5) Integer
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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New post 07 Feb 2014, 22:01
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Step 1- Keep X =0 and solve for Y

Step 2- Keep Y=0 and Solve for X..


B--- give non integer i.e x= -1/2 and Y= 1/2
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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New post 08 Feb 2014, 04:49
SOLUTION

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5

The answer is y=x+1/2, since for any integer value of x, y becomes integer and a half: .

Answer: B.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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New post 15 Jun 2017, 16:22
Just Plot the line for each option . We will get a clear ans as B .
How to plot ?
to get y , put x=0
and to get x , put y=o and then join the points to get the line .
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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New post 09 Aug 2017, 09:48
For option D & E; What values to consider for x, y. Is it ok to consider values as 0??
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5


We see that the point (1,1) is on the line y = x (answer choice A); (1, 6) on y = x + 5 (C); (2, 1) on y = x*1/2 (D); and (2, 6) on y = x/2 + 5 (E). Thus, the only line that won’t have any point with integers as both coordinates is y = x + 1/2 (answer choice B). The reason is simple: if x is an integer, then y can’t be an integer, since the sum of an integer and 1/2 will never be an integer. Similarly, if y is an integer, then x can’t be an integer, since the difference of an integer and 1/2 (notice that x = y - 1/2) can never be an integer.

Answer: B
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Re: Which of the following lines in the xy-plane does not contai [#permalink]

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New post 05 Mar 2018, 07:52
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?

(A) y = x
(B) y = x + 1/2
(C) y = x + 5
(D) y = x*1/2
(E) y = x/2 + 5

Problem Solving
Question: 83
Category: Algebra; Arithmetic Substitution; Operations with rationa l numbers
Page: 72
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


can someone explain what the question is asking about? and what is the logic behind solution ? i dont get.

i know this formula y = mx + b where

m is slope

b is y-intercept
Re: Which of the following lines in the xy-plane does not contai   [#permalink] 05 Mar 2018, 07:52
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