1. tells you that w + 2 > 0, so w > -1. Not sufficient to know whether w is greater than 1.
2. w^2 > 1 means that w^2 - 1 > 0
w^2 - 1 > 0
(w - 1)(w + 1) > 0
This is a quadratic equation with two roots, -1 and 1. The quadratic equation is only positive outside the roots, so w is either smaller than -1 or greater than 1.
Another way of looking at this is to notice that 1 is the square of both 1 and -1. w^2 > 1 means that you can have either w < -1 (take w = -2 for instance) or w > 1 (take w = 3).
As you can see, 2 yields two possible intervals for w, so it's not enough either.
But put both together and using the fact that w > -1 from stmt 1 eliminates one interval from stmt 2, leaving only w > 1. C is your answer here.
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GMATprep: Is w > 1?
Source: Beat The GMAT — Data Sufficiency |
The first statement is actually saying w>-2. I think you did a typo & followed it up to your answerDanaJ wrote:1. tells you that w + 2 > 0, so w > -1. Not sufficient to know whether w is greater than 1.
2. w^2 > 1 means that w^2 - 1 > 0
w^2 - 1 > 0
(w - 1)(w + 1) > 0
This is a quadratic equation with two roots, -1 and 1. The quadratic equation is only positive outside the roots, so w is either smaller than -1 or greater than 1.
Another way of looking at this is to notice that 1 is the square of both 1 and -1. w^2 > 1 means that you can have either w < -1 (take w = -2 for instance) or w > 1 (take w = 3).
As you can see, 2 yields two possible intervals for w, so it's not enough either.
But put both together and using the fact that w > -1 from stmt 1 eliminates one interval from stmt 2, leaving only w > 1. C is your answer here.
IMO E.
I just plugged number in this one. (also notice that w is not an integer)
1) w + 2 > 0 Is clearly insufficient. (ex. w = 1 or w = 2)
2) w^2 > 1 is also insufficient (ex. w = 5 or w = -5)
together, w can be 3 and can be sufficient.
but if w = -3/2
-3/2 + 2 > 0 (satsfies)
(-3/2)^2 = 9/4 > 1(satisfies)
but -3/2 is not > 1: therefore Insufficient.
(E)
I just plugged number in this one. (also notice that w is not an integer)
1) w + 2 > 0 Is clearly insufficient. (ex. w = 1 or w = 2)
2) w^2 > 1 is also insufficient (ex. w = 5 or w = -5)
together, w can be 3 and can be sufficient.
but if w = -3/2
-3/2 + 2 > 0 (satsfies)
(-3/2)^2 = 9/4 > 1(satisfies)
but -3/2 is not > 1: therefore Insufficient.
(E)
