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# M06-04

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09 Jun 2012, 03:25
Quantitative :: Data sufficiency :: M06-04
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If g is an integer what is the value of (−1)^(g^4−1)?

(1) g^2<1

(2) g^2+2g−3<0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH stamenents TOGETHER are sufficient, but NEITHER stamenent ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Mark as a guess Hide Answer

(1) g^2<1 → since g is an integer then g=0. Sufficient to calculate the value of (−1)g4−1.

(2) g^2+2g=0 → g(g+2)=0 → g=0 or g=−2. Since both possible values of g are even then (−1)even4−1=(−1)even−1=(−1)odd=−1. Sufficient.

------------------------------------------------------

I answered A. This question has a problem. (2) g^2+2g−3<0 ---->> g= -1 or g=3, how come the solution changes the equation totally??
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09 Jun 2012, 03:29
heintzst wrote:
Quantitative :: Data sufficiency :: M06-04
Flag for Review
If g is an integer what is the value of (−1)^(g^4−1)?

(1) g^2<1

(2) g^2+2g−3<0

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH stamenents TOGETHER are sufficient, but NEITHER stamenent ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Mark as a guess Hide Answer

(1) g^2<1 → since g is an integer then g=0. Sufficient to calculate the value of (−1)g4−1.

(2) g^2+2g=0 → g(g+2)=0 → g=0 or g=−2. Since both possible values of g are even then (−1)even4−1=(−1)even−1=(−1)odd=−1. Sufficient.

------------------------------------------------------

I answered A. This question has a problem. (2) g^2+2g−3<0 ---->> g= -1 or g=3, how come the solution changes the equation totally??

There is typo. Will be edited ASAP. Thank you for pointing out.
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Manager
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07 Jul 2012, 08:37
Guys please correct me if I am wrong

g^4-1 = g^4/g = g^3 therefore we are concerned about the value of g^3, as if it yields an even number the answer will become 1

1.- g^2 < 1 There is no other number rised to the power of two that yields a negative result, so g = 0, sufficient

2.- x= -1 or x = 3, as each of the results is odd, it is sufficient to realize that the value of g is -1.

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07 Jul 2012, 09:29
hi
statement 1 is sufficient as mentioned in earlier replies.
as for stat 2.. g^2+2g−3<0
(g+3)(g-1)<0 so g can be -2,-1,0, or 1.....
when we substitute -2 or 0 ans is -1..... however -1 and 1 will give us 1 as anything raised to power 0 is 1... A shud be the ans
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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07 Jul 2012, 09:32
Bull78 wrote:
Guys please correct me if I am wrong

g^4-1 = g^4/g = g^3 therefore we are concerned about the value of g^3, as if it yields an even number the answer will become 1

1.- g^2 < 1 There is no other number rised to the power of two that yields a negative result, so g = 0, sufficient

2.- x= -1 or x = 3, as each of the results is odd, it is sufficient to realize that the value of g is -1.

it is (g^4)-1 and not g^(4-1)
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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07 Jul 2012, 10:30
Correct question with a solution is below:

If $$g$$ is an integer what is the value of $$(-1)^{g^4 - 1}$$ ?

(1) $$g^2<{1}$$ --> since $$g$$ is an integer then $$g=0$$. Sufficient to calculate the value of $$(-1)^{g^4 - 1}$$.

(2) $$g^2+2g=0$$ --> $$g(g+2)=0$$ --> $$g=0$$ or $$g=-2$$. Since both possible values of $$g$$ are even then $$(-1)^{even^4 - 1}=(-1)^{even-1}=(-1)^{odd}=-1$$. Sufficient.

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Re: M06-04   [#permalink] 07 Jul 2012, 10:30
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# M06-04

Moderator: Bunuel

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