M06-04

Question

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.
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(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.

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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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Bunuel · Answer

There is typo. Will be edited ASAP. Thank you for pointing out.

Bull78 · Answer

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.

So answer is still D

chetan2u · Answer

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

chetan2u · Answer

it is (g^4)-1 and not g^(4-1)

Bunuel · Answer

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.

Answer: D.

M06-04

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