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coordinate geo

by nafiul9090 » Fri Mar 16, 2012 5:49 pm
In the xy- plane, region A consists of all the points (x,y) such that 1-x<2y. is the point (a,b) in the region A?

i) a>2b
ii) b=1

total confused

if i simplifying the inequality thn i found b> (-1/2)a + 1/2 what i do thn??

oa is c
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Source: — Data Sufficiency |
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by Neo Anderson » Sat Mar 17, 2012 5:05 am
hey friend, could crack it with coordinate geometry....

the graph of 1-x<2y will appear as in figure (question)...Image

from statement 1 => a>2b we get region shown in figure (statement 1)....
Image
as the new region partly overlaps the original region => hence insufficient

from statement 2=> b=1 we get the region shown in the figure (statement 2)....
Image
as the new region partly overlaps the original region => hence insufficient

taking both together we get the 3rd figure (both statements)
Image
we can see that the region beyond this point( b=1 and a>2) for sure lies on the original region => both together are sufficient to answer the question!! hence c!
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by [email protected] » Sat Mar 17, 2012 5:42 am
Whatever
Neo Anderson
has written as the solution is the correct answer....

there is no other alternative to solve this kind of questions,,,

The correct answer is C. Just be a bit careful in not doing any silly mistakes in these questions...
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by tomada » Sat Mar 17, 2012 10:51 am
I used an alternative approach. Since our time is heavily constrained, I try to avoid drawing graphs unless absolutely necessary.

Statement 1: a>2b

let's say b=0.
Now, any positive value of 'a' will satisfy Statement 1.

Substituting 'b' for 'y', which we can do since (a,b) corresponds to (x,y), we have the following:

1-x < 2(0), or 1-x < 0.

Another way to say this is "1-a < 0".
If a > 1, this is true.
If 1 > a > 0, this is false

Statement 1 is insufficient.

Statement 2: b=1

Substituting 'b' for 'y', we get the following:

1-x < 2(1), or 1-x < 2

Another way to say this is "1-a < 2"

If a > -1, this is true
If a <= -1, this is false

Statement 2 is insufficient.

Combining the two statements, we know that:

b = 1
a > 2

Another way of saying this is:

y = 1
x > 2

From the original equation (or Statement 2), "1 - x < 2".

Since x > 2, any such value of 'x' will satisfy this statement.

Combining Statements (1) and (2) is sufficient
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by Neo Anderson » Sat Mar 17, 2012 8:27 pm
quite convincing!
thanks for the alternative approach....
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by GMATGuruNY » Sat Mar 17, 2012 9:45 pm
nafiul9090 wrote:In the xy- plane, region A consists of all the points (x,y) such that 1-x<2y. is the point (a,b) in the region A?

i) a>2b
ii) b=1

total confused

if i simplifying the inequality thn i found b> (-1/2)a + 1/2 what i do thn??

oa is c
For (a,b) to be in region A, it must satisfy 1-x < 2y:
1-a < 2b
1 < a + 2b.

Question rephrased: Is a + 2b > 1?

Statement 2: b=1
No information about a.
INSUFFICIENT.

Statement 1: a > 2b
Plugging a=2 and 2b=1 into a+2b > 1, we get:
2 + 1 > 1?
3>1.
YES.

Plugging a=0 and 2b= -1 into a+2b > 1, we get:
0 + (-1) > 1?
-1>1.
NO.

Since in the first case the answer is YES, and in the second case the answer is NO, INSUFFICIENT.

Statement 1 and 2 combined:
Since b=1 and a>2b:
a > 2(1)
a + 2b > 2(1) + 2(1)
a + 2b > 4.
SUFFICIENT.

The correct answer is C.
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