Are x and y both positive


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

OA is C

Hi anjali,

I hope that you are familiar with equation of a line and a bit of geometry.

Now just look at the equation 2x-2y=1 which is equal to y=x-0.5 which is an equation of a line.This line will pass through the first , third and the fourth quadrant in a rectangular co-ordinate system(you can roughly draw it and see) which means that x and y need not always be positive though the equation can be satisfied by both x and y being positive at the same time.

Looking at x/y>1 one thing we can be sure of is that magnitude of x must be greater that y and x/y must be positive.
But a negative number divided by a nagative number is also positive.Hence x and y need not always be positive at the same time.

The first clue clarifies that x and y both can be positive(first quadrant) or x positive and y negative(fourth quadrant) or x negative and y negative(third quadrant).
The second clue clarifies that either both are positive or both are begative.

I don't think either of the clues give a certain answer about both being always positive at the same time.

Start by plugging numbers

x - y = 0.5

x= 1.5, y = 1, then x - y = 0.5. so x>0 and y>0

x = -0.5 and y = 1, then y = 0.5 but x<0 and y > 0

Insufficient

Statement 2

Does add much

But if you combine both, we see x can't be negetive

Hence C

I may have missed something but I think there were some inaccuracies above.

-.5 and 1 do not work as solutions for x and y respectively in A. 2(-.5) -2(1) = 1 (-3 <> 1)

If you put in -.5 and -1 that will give you a solution. but positive 2 and 1.5 will also work so x and y can be either neg or pos. (insufficient)

b) this tells that x and y are either both neg or both pos also and that the abs value of x is larger than abs value of y.

Combining the 2 since x has be larger than y, the only way (a) would work is with positive numbers. Hence (C).

St:1
2(X-Y)=1
X-Y=0.5
St:2
X and Y have the same sign. nothing more

Together=1+2
X-Y
1-0.5=0.5 (both X and Y are positive)
-0.5-(-1)=0.5(both X and Y are negative)
now 1/0.5=2>1
-0.5/-1=0.5<1
so answer is C
i think this will help

GMAT Staff please help.

We have 3 different answers. I think guest_z nailed it :) but could you confirm what the right approach would be?

think it easy:
1) x-y=1/2 .. Positive => x>y since can be: (+,+) or (+,-) or (-,-) : Insuff

2) x/y>1 since x/y>0 since (x,y) have to have the same sign: (-,-) or (+,+) : Insuff

Let's see what we could earn putting together:

2) finding the conditions of existence of the second expression we find that to exist, the expression is x>y for (+,+) and x<y when (-,-) that excludes the ambiguity and put the focus on the case (+,+).

Explaining what I meant: "Dear High School math that with inequalities is unequaliable":
x/y>1 => (x-y)/y > 0 => True if (x-y) have the same sign of y so:

· y>0 => x>y in agreement with what implied in the statement 1
· y<0 => x<y in disagreement with what implied in the first statement.

Hope not to have confuse you...
I'll leave to Magic Ron the duty to explain the answer in his full clearness.

Andrea

My approach as following :

1. x - y = 1/2 => x = y + 1/2. Y can be either positive or negative, therefore X can be + or - number. --- Not sufficient

2. x/y > 1 implies that X and Y has to be of same sign, either both positive or both negative. -- not sufficient

Combining (1) and (2), infact substituting (1) in (2)
(y + 1/2)/Y > 1 => 1 + (1/2y) > 1
Substracting 1 from both sides will give (1/2y) > 0, which means Y has to be positive.
This inturn means X has to be positive.

Hence answer is (c)

Easy and Efficient!
that grinds the question without too much reasonings

well done.

--

here's a good way to deal with x/y > 1 in ALL situations:
break it into 2 cases: x and y both positive vs. x and y both negative.
if x and y are both positive, then multiplying by y doesn't change the sign, so, x > y.
if x and y are both negative, then multilplying by y does change the lign, so, x < y.
therefore, statement (2) means either x > y > 0 or x < y < 0.

statement (1) implies that x is bigger than y, so this means that, together, the statements mean x > y > 0.
answer (c).