Is w > 1?
(1) w + 2 > 0
(2) w^2 > 1
Please help me with this one.
E
GMATprep: Is w > 1?
This topic has expert replies
- DanaJ
- Site Admin
- Posts: 2567
- Joined: Thu Jan 01, 2009 10:05 am
- Thanked: 712 times
- Followed by:550 members
- GMAT Score:770
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.
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.
- Vemuri
- Legendary Member
- Posts: 682
- Joined: Fri Jan 16, 2009 2:40 am
- Thanked: 32 times
- Followed by:1 members
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.
- ssmiles08
- Master | Next Rank: 500 Posts
- Posts: 472
- Joined: Sun Mar 29, 2009 6:54 pm
- Thanked: 56 times
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)