Algebra Question

[Spartacus2000]

Are x and y both positive?

(1) 2x - 2y = 0
(2) x/y > 0

How is statement (1) to be used to come to the answer?

[cans]

to find if both x,y>0
a) 2x-2y=0 or 2x=2y or x=y
it means they can both be negative, or positive or zero.
insufficient.
b) x/y>0
if x=1, y =2; 1/2>0 true
if x=-1,y=-2; -1/-2=1/2>0 true
hence we can't say they both are positive. Insufficient.
Both A & B together: x=y and x/y = y/y = 1 which is always greater than 0,
Thus insufficient.
IMO E

[SoCan]

As cans said, statement 1 just means that x and y are equal, but they could be positive or negative.

For the second statement - a quick way to think about x/y>0 is that the sign of x and y are the same. You don't have to spend time plugging in numbers - just ask yourself if knowing that both signs are the same is sufficient to answer the question.

[Spartacus2000]

My mistake.

The first statement is 2x - 2y = 1.

Sorry about that.

[cans]

My mistake.

The first statement is 2x - 2y = 1.

Sorry about that.

a)2x-2y=1 => x = y + 1/2
x&y can be of any sign. For ex (x,y): (0,-1/2) (1,1/2) (-1/2,-1) and so on....
Insufficient.

b)x/y>0 => x and y are of same sign. Either both are positive or both are negative
Thus insufficient.

a & b together) x= y + 1/2 and x,y have same sign.
still insufficient as (1,1/2) & (-1/2,-1) both satisfy these conditions.
Thus IMO E

[pemdas]

-1=-1/2+1/2 doesn't satisfy the condition 2x-2y=1

from statement (1) x is greater than y, as x=y+1/2 for the positive signs, and x is less than y for the negative signs.
from statement (2) x/y>0 is true for all non-zero y, when x is greater than y for the positive signs, and x is less than y for the negative signs.
combining both statements we get the same conditions, hence no restriction for x and y as being positive.

it must be e

My mistake.

The first statement is 2x - 2y = 1.

Sorry about that.

a)2x-2y=1 => x = y + 1/2
x&y can be of any sign. For ex (x,y): (0,-1/2) (1,1/2) (-1/2,-1) and so on....
Insufficient.

b)x/y>0 => x and y are of same sign. Either both are positive or both are negative
Thus insufficient.

a & b together) x= y + 1/2 and x,y have same sign.
still insufficient as (1,1/2) & (-1/2,-1) both satisfy these conditions.
Thus IMO E

[cans]

-1=-1/2+1/2 doesn't satisfy the condition 2x-2y=1

from statement (1) x is greater than y, as x=y+1/2 for the positive signs, and x is less than y for the negative signs.
from statement (2) x/y>0 is true for all non-zero y, when x is greater than y for the positive signs, and x is less than y for the negative signs.
combining both statements we get the same conditions, hence no restriction for x and y as being positive.

it must be e

My mistake.

The first statement is 2x - 2y = 1.

Sorry about that.

a)2x-2y=1 => x = y + 1/2
x&y can be of any sign. For ex (x,y): (0,-1/2) (1,1/2) (-1/2,-1) and so on....
Insufficient.

b)x/y>0 => x and y are of same sign. Either both are positive or both are negative
Thus insufficient.

a & b together) x= y + 1/2 and x,y have same sign.
still insufficient as (1,1/2) & (-1/2,-1) both satisfy these conditions.
Thus IMO E

I never used(-1,-1/2) as a point. I was other way round (-1/2,-1)

[pemdas]

ok, (1,1/2) and (-1/2,-1) are still (x,y)? the values are changing with signs then
that's the reason i posted above
and Yes, with (-1/2;-1) works for both statements, BUT then (1/2;1) doesn't work again

you are changing not only signs but values too in your example, agree?

-1=-1/2+1/2 doesn't satisfy the condition 2x-2y=1

from statement (1) x is greater than y, as x=y+1/2 for the positive signs, and x is less than y for the negative signs.
from statement (2) x/y>0 is true for all non-zero y, when x is greater than y for the positive signs, and x is less than y for the negative signs.
combining both statements we get the same conditions, hence no restriction for x and y as being positive.

it must be e

My mistake.

The first statement is 2x - 2y = 1.

Sorry about that.

a)2x-2y=1 => x = y + 1/2
x&y can be of any sign. For ex (x,y): (0,-1/2) (1,1/2) (-1/2,-1) and so on....
Insufficient.

b)x/y>0 => x and y are of same sign. Either both are positive or both are negative
Thus insufficient.

a & b together) x= y + 1/2 and x,y have same sign.
still insufficient as (1,1/2) & (-1/2,-1) both satisfy these conditions.
Thus IMO E

I never used(-1,-1/2) as a point. I was other way round (-1/2,-1)