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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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New post 07 Feb 2014, 05:47
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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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(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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New post 07 Feb 2014, 12:52
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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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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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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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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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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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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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New post 14 Aug 2017, 15:22
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] 14 Aug 2017, 15:22
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