gmat prep - how do i solve this

[anjali]

Are x and y both positive


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

OA is C

[michael_shaunn]

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.

[Khalid]

Are x and y both positive


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

OA is C

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

[guest_z]

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).

[shobuj40]

Are x and y both positive


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

OA is 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

[guest_z]

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?

[AndreaDB]

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

[kanaks123]

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)

[AndreaDB]

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

[RonPurewal]

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)

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).