Is point (a, b) above line y=x?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 23, 2013 3:22 pm

Hello,

Can you please assist with this:

In a rectangular coordinate system, if a and b are positive integers, is point (a, b)
above line y = x?

1) a = 4
2) b = a + 2

OA: B

I am clear with 1 but not with 2. Can you please assist?

Thanks,
Sri

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 23, 2013 3:22 pm

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by [email protected] » Sat Nov 23, 2013 3:32 pm

Hi Sri,

I'm going to give you a hint and let you try Fact 2 again.

1) Draw a graph.
2) Graph the equation Y = X.

3) Notice how A and B are POSITIVE INTEGERS.
4) Fact 2: B = A + 2
5) TEST Values and then graph them. **Remember, A and B are POSITIVE INTEGERS.**

6) Are all of your co-ordinates above the line?

GMAT assassins aren't born, they're made,
Rich

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 23, 2013 5:03 pm

[email protected] wrote:Hi Sri,

I'm going to give you a hint and let you try Fact 2 again.

1) Draw a graph.
2) Graph the equation Y = X.

3) Notice how A and B are POSITIVE INTEGERS.
4) Fact 2: B = A + 2
5) TEST Values and then graph them. **Remember, A and B are POSITIVE INTEGERS.**

6) Are all of your co-ordinates above the line?

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Thanks for your help. I followed your points and came up with the following graph. So I think all the points (a,b) are above the line y = x. Can you please tell me if this graph is OK?

Also, I wanted to know what points would fall on the line y = x? I am thinking that the equation of the line would be y = mx + c. However, since y-intercept is 0, c = 0. Hence, y = mx. I was wondering how the slope of this line would be 1 so that we get y = x. I was just wondering if you can please explain this? Thanks for your help - Sri

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by [email protected] » Sat Nov 23, 2013 8:16 pm

Hi Sri,

Your picture is fine (although it's not exactly to scale); it provides the proof that every possible value of (a,b) is above the line Y = X.

For a co-ordinate to be ON the line, then X would have to equal Y. With the information from the prompt, we know that A and B are POSITIVE INTEGERS, which eliminates the possibility of negatives, zeroes and fractions.

With the added info in Fact 2: B = A + 2, it means that B will NEVER equal A, so every co-ordinate (A, B) that you can come up with will NOT be on the line (they will all be ABOVE it because the B is 2 more than the A).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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