DS - GMATPrep - (are x and y both positive)

[winna.7]

hey guys? does GMAT Prep actually have errors? i mean ..even i came across this problem that i foud erroneous. Cant post it here because i am not alowed to post attachments yet.

By the way, the answer for the above is C.

[rajibgmatNJ]

Originally Posted by jaybird

nick,

remember when you get stuck the next best thing is to plug in numbers.

So check it:

Are x and y both positive?

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


Part I: 2x - 2y = 1 is the same as 2(x-y) = 1.

If we plug in 1/4 for "X" and (-1/4) for "Y" we get

2(1/4 - (-1/4) = 1. This is true. If we plug in: 2 for "X' and 3/2 for "Y" we get:
2(2 -3/2) = 1. Once again this is true. So here, X and Y can be both positive, or X can be positive and Y can be negative.

Insufficient:

Part II states: x/y > 1

Here X and Y can both be negative: -5/-4 = 5/4 which > 1. Or they can both be positive. 5/4 > 1.

Once again insufficient.

Combine both equations:

Equation 1 says: (X and Y are both positive) or (X is positive and Y is negative)
Equation 2 says: (X and Y are both positive) or (X and Y are negative)

(X are Y are positive) allows both equations to be true. Therefore C is sufficient.

Equation 1 can have scenario where both x and y can be negative.
For example, x = -4.5 and y = -5 => x-y = -4.5 - (-5) = 0.5 (1/2)

So your solution fails here....jaybird

[rajibgmatNJ]

Originally Posted by vnf

Are x and y both positive?

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

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

If y > 0 => x > y => x - y > 0
If y < 0 => x < y => x - y < 0

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

Hence, (C)

Great explanation...dude

[cambridgedove]

I think the sum of n odds is equal to n^2. Probably doesn't help if you've never dealt with series before, but it is one of the easier ones. I guess that isn't entirely helpful unless you also know/can figure out the nth odd, which is just 2n-1

Here I'd just solve 2n-1=991 => n=992/2=496
n^2=496^2=246016

If you practice with sequences and series like these it'll only take plugging in a couple of numbers to remember the pattern, and they're good practice for mathematical induction if you care about math. If you want to keep this one gangster, show 1=1^2 then the induction step would be assume sum of n odds = n^2 => sum of n odds + (2n-1)+2 = n^2+(2n-1)+2 => sum of n+1 odds = (n+1)^2 QED