Data Sufficiency

It's from the Prep test:

Are x and y both positive?

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


It's probably easy, but I don't see how you can answer the question with these two equations.

Thanks,

mr T

1) 2x - 2y = 1

From above x - y = 1/2

So x > y....Insufficient...as both can be +ve or -ve

2) x / y > 1

Insufficient as both can be +ve or -ve.

Combined,

x > y from 1

and from 2, y needs to be +ve for 1 to be true (else we would have y>x),
so it follows that both x and y are +ve.

Hence C.

What's the OA?

Answer - C

Can someone spot the error here?

From (1), x - y = 1/2
From (2), x/y > 1 so x > y

Choose x= 1/2 and y = -1/2 to satisfy both 1 and 2. So x and y cannot be both positive?

Please enlighten.

valleeny wrote:Can someone spot the error here?

From (1), x - y = 1/2
From (2), x/y > 1 so x > y

Choose x= 1/2 and y = -1/2 to satisfy both 1 and 2. So x and y cannot be both positive?

Please enlighten.

What did you assume here?

kevincanspain wrote:

valleeny wrote:Can someone spot the error here?

From (1), x - y = 1/2
From (2), x/y > 1 so x > y

Choose x= 1/2 and y = -1/2 to satisfy both 1 and 2. So x and y cannot be both positive?

Please enlighten.

What did you assume here?

I'm sorry. I may have poor basic understanding but isn't x/y>1 equate to x>y? Multiply both sides by y.

valleeny wrote:

kevincanspain wrote:

valleeny wrote:Can someone spot the error here?

From (1), x - y = 1/2
From (2), x/y > 1 so x > y

Choose x= 1/2 and y = -1/2 to satisfy both 1 and 2. So x and y cannot be both positive?

Please enlighten.

What did you assume here?

I'm sorry. I may have poor basic understanding but isn't x/y>1 equate to x>y? Multiply both sides by y.

Hi

In the equality the multiplying on the both the sides with some number has to done very carefully.The sign will remain same if multiplied by the positive no,It will be reversed if multiplied by negative numbers.

Illustrating with your example only.
x/y>1

Suppose x=3 and y=2, You can multiply both side by y in present situation so x>y and equation will hold good with the value of x and y as assumed

Now suppose x=-3,y=-2;Now if you take the equation and multiply both side by y,then it will become x<y(and not x>y)

Hence bottom line is that if you are not sure, do not multiply and divide the inequality with unknown variables.


Thanks

Mr_T wrote:It's from the Prep test:

Are x and y both positive?

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


It's probably easy, but I don't see how you can answer the question with these two equations.

Thanks,

mr T

Simple Approach

Statement 1: x-y=1/2
Either both are positive or both are negative... Not clear... Insufficient

Statement 2: X/Y>1
Either Both are positive or both are negative for this to be true... Not clear... Insufficent
Also, absolute value in numerator has to be > denominator. But that does not rule out the possibility of either being positive or negative...not Clear... Insufficient
In any case... |x|>|y| for this condition to be true

Jointly
For x/y>1, there are only two conditions
a. If both are positive; which satisfies equation 1
b. If both are negative, with |x|>|y|; which makes the equation 1 impossible to be true
e.g. if X=-7/2 and Y=-3.. Equation 1 will be -7/2+3=-1/2 and not 1/2 as the equation prescribes

So decisively, Both are positive... Hence C

Alternatively
if X-Y=1/2, there are only two possibilities
a. If both are positive. Then, Clearly X>Y... Satisfies equation 2
b. If both are negative. Then, |y|>|x|...and condition 2 is opposite of this (|x|>|y|)... Not possible...

So decisively, Both are positive... Hence C

Thanks guys!

I too made the mistake of blindly multiplying variables on both side of inequality equations. I'll only do that with constants from now on.

Thanks,

mr T