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In the xy plane does the point (a, b) lie above the line y=x

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In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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In the xy plane, does the point (a, b) lie above the line y=x?

(1) a=2
(2) b=a+2
[Reveal] Spoiler: OA

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Re: n the xy plane, does the point(a, b) [#permalink]

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monir6000 wrote:
In the xy plane, does the point(a, b) lie above the line y=x?
(1) a=2
(2) b=a+2


used substitution method

given that y = x

1) a=2, no mention of b

so the point (a,b) can fall either below the line or above the line y=x

so NS .. hence Options A & D are gone.

2) b = a+2
so take any value a, b will be greater than a by 2...

hence this point will always be above the line... Hence B....
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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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In the xy plane, does the point (a, b) lie above the line y=x?

Each point of line y=x has the same x and y coordinates: (-7, -7), (1, 1), (100, 100), ...

(1) a=2. Not sufficient since no info about b

(2) b=a+2 --> since y coordinate of the point is 2 more than its x coordinate than it will lie above the line x=y, consider point (1, 3). Sufficient.
Attachment:
y=x.png
y=x.png [ 12.4 KiB | Viewed 5968 times ]


Answer: B.
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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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New post 25 Apr 2012, 00:06
Thanks Bunnel & harshavmrg.......
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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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New post 21 Sep 2015, 22:46
if the value of a was -4, will answer choice b still be the answer? such that point a will be -4 and b equals -2 (ie -4+2). Am thinking the line will then be under the x=y line

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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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New post 19 Aug 2016, 19:23
Have a query, in the prompt it is mentioned that point lies above the line 'y=x', so only positive values of 'a' to be considered.? Because if negative values are considered then statement 2 won't be sufficient.

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Re: In the xy plane does the point (a, b) lie above the line y=x [#permalink]

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New post 01 Oct 2016, 22:45
There is a very interesting concept that I have learnt.
Any point above the line x=y will have higher value of y as compared to x and any point below the line x=y will have lower value of y as compared to x so the question generally boiled down to if b>a and statement 2 proved it to be correct
IMO B

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Re: In the xy plane does the point (a, b) lie above the line y=x   [#permalink] 01 Oct 2016, 22:45
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In the xy plane does the point (a, b) lie above the line y=x

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