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

Question

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

(1) a=2
(2) b=a+2

Bunuel · Accepted Answer

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 [ 12.4 KiB | Viewed 19337 times ]

Answer: B.

harshavmrg · Answer

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....

monir6000 · Answer

Thanks Bunnel & harshavmrg.......

Tos · Answer

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

narendran1990 · Answer

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.

AmritaSarkar89 · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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