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bourneJ: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Mon Jun 13, 2011 6:14 am

by bourneJ » Wed Jul 13, 2011 9:17 pm

Question 83: 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

Can someone please tell me what is it that the question is asking?
Answer B

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Source: Beat The GMAT — Problem Solving | Wed Jul 13, 2011 9:17 pm

krishnasty: Master | Next Rank: 500 Posts; Posts: 142; Joined: Mon Jan 10, 2011 8:03 am; Thanked: 19 times

by krishnasty » Wed Jul 13, 2011 9:46 pm

IMO B

the question is asking that if we have a line which is defined by the below options, on which line, would we not have both the coordinates as integers.
in other words, for which line, would we have one coordinate as integer and one as fraction.
best way - plug in the numbers.

bourneJ wrote:Question 83: Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?
A) y=x x = 2, hence y =2..both integers
B) Y=x+1/2 x = 2, y = 3/2. correct option
C) Y=x+5 x = 2, y = 7. both integers
D) y=x.1\2 x = 4, y = 2 both integers
E) y=x/2 +5 x = 4, y = 7.. both integers

Can someone please tell me what is it that the question is asking?
Answer B

i hope ans is much clear now

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Appreciation in thanks please!!

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Wed Jul 13, 2011 9:48 pm

a y=x=1 is possible. POE.
b y will be always = x+0.5. hence for x=1 y=0.5. Hold it.
c for x=1,2 any value y can be integer. POE.
e x=2 gives y=6. hence POE.

question is asking which of these equations will always give non integer value for xor y or both x and y.Hence substitute values and check as above.

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aplavakarthik: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Thu Jul 07, 2011 2:16 am; Thanked: 2 times

by aplavakarthik » Fri Jul 15, 2011 6:21 am

Hi,

The question is asking about which line equation passes through XY plane and having x coordinate or y coordinate which is equal to an integer.

check the X intercept and Y intercept of the given equations if the X\Y intercept is an integer that is not our answer.

we know that Y=mx+c, c is Y intercept and y=0 in the equation gives X intercept

Option A: Y=X
has both intercepts (0,0), Integer value

Option B: Y=x+1/2
y Intercept =1/2 and x intercept =-1/2
not integers and so this is the answer.

Option C: Y=x+5
Y Intercept =5, Integer Value

Option D: y=x.1\2
Y Intercept=X intercept =0, Integer Value

Option E:y=x/2 +5
Y Intercept =5, Integer Value

So, finally On B satisfies

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