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Stockmoose16
- Master | Next Rank: 500 Posts
- Posts: 347
- Joined: Mon Aug 04, 2008 1:42 pm
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Hi,
I'm having a difficult time with number properties DS questions, like the following:
Is xy > 0 ?
1) x - y > -2
2) x - 2y < -6
OA is C
Ron Purewell from MGMAT showed how to do this problem on the MGMAT Forum, but I'm unclear as to how he decided upon which numbers to pick. I'm always worried I'm going to miss something. For example, "If you select integers, would the answer come out differently if you selected fractions?" Or, "What if X is larger than Y"... "What if one is negative and one is positive?" By the time I prove each statement sufficient or insufficient, I've completely lost my place. If both are insufficient, I find it nearly impossible to decide between C & E, because the information is so garbled in my mind.
Here's how Ron Purewell explained how to do the above problem:
ok, well, first establish that (a) and (b) <i>individually</i> are insufficient by testing cases:
(1)
x = y = 1 --> yes
x = y = 0 --> no
insufficient
(2)
x = y = 100 --> yes
x = -10, y = 10 --> no
insufficient
so think about the two statements together:
SWITCH THE SIGNS of the latter inequality, so that the signs face the same way:
x - y > -2
-x + 2y > 6
add them (note that you can add inequalities whose signs are facing the same way - a useful fact):
y > 4
this means y is positive.
back to the first inequality
x > -2 + y
since y is more than 4, this means that x is more than 2
so x is positive
so x and y are both positive.
How did he decide upon the different sets of numbers used to prove/disprove statement #1 and statement #2? How did he know not to test fractions? What about if X were bigger than Y and visa versa, why didn't he test those scenarios? What if one number were negative and the other were positive?
You see, by the time you think all these things through, you would be out of time (by a long shot). I'm thinking Ron knew which smart numbers to pick based on the information given. I would've tried to test every possible scenario, and never would've finished the question in time.
Can anyone offer some insight?
I'm having a difficult time with number properties DS questions, like the following:
Is xy > 0 ?
1) x - y > -2
2) x - 2y < -6
OA is C
Ron Purewell from MGMAT showed how to do this problem on the MGMAT Forum, but I'm unclear as to how he decided upon which numbers to pick. I'm always worried I'm going to miss something. For example, "If you select integers, would the answer come out differently if you selected fractions?" Or, "What if X is larger than Y"... "What if one is negative and one is positive?" By the time I prove each statement sufficient or insufficient, I've completely lost my place. If both are insufficient, I find it nearly impossible to decide between C & E, because the information is so garbled in my mind.
Here's how Ron Purewell explained how to do the above problem:
ok, well, first establish that (a) and (b) <i>individually</i> are insufficient by testing cases:
(1)
x = y = 1 --> yes
x = y = 0 --> no
insufficient
(2)
x = y = 100 --> yes
x = -10, y = 10 --> no
insufficient
so think about the two statements together:
SWITCH THE SIGNS of the latter inequality, so that the signs face the same way:
x - y > -2
-x + 2y > 6
add them (note that you can add inequalities whose signs are facing the same way - a useful fact):
y > 4
this means y is positive.
back to the first inequality
x > -2 + y
since y is more than 4, this means that x is more than 2
so x is positive
so x and y are both positive.
How did he decide upon the different sets of numbers used to prove/disprove statement #1 and statement #2? How did he know not to test fractions? What about if X were bigger than Y and visa versa, why didn't he test those scenarios? What if one number were negative and the other were positive?
You see, by the time you think all these things through, you would be out of time (by a long shot). I'm thinking Ron knew which smart numbers to pick based on the information given. I would've tried to test every possible scenario, and never would've finished the question in time.
Can anyone offer some insight?
