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What is the value of (-1)^{g^4 + g - 1} ? 1. g is an [#permalink]
 21 Dec 2008, 09:55
What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer 2. g is even * 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient Source: GMAT Club Tests - hardest GMAT questions shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right?
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you have to realize that if you have fractions then we will have a imaginary number and that we dont consider in GMAT.
so 1) is sufficient..if g is ODD, and even it its negative
if g=1, then (-1)^1 if g=-1, g= (-1)^-1 i.e 1
if g=2 then (-1)^odd is -1..
so sufficient
2) sufficient..
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Director
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I think I miss calculated ... thanks for the correction ...
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Why 1) Sufficient? It is either 1 or -1 so we can't tell...While 2) is definitely -1
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Director
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I too was thinking in the same way when i was taking the test that statement can be 1 or -1 .... but looks like I am not able to get +1 scenario no w... can you write up ur test case which produces +1?
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FYI - here is the latest official explanation (not updated yet in the tests database - we are editing them offline).
Let me know if you have any comments about qualityStatement (1). Sufficient. If g is an integer, for any value of g (positive or negative or zero), the end result will always be (-1). That's because we subtract 1 from an always even number (which means the exponent will never be 0, even if g = 0). Therefore, (-1) will be always taken to an odd power, and the expression will always result into (-1), as long as g is an integer. For example: let's try 3 and 2 as values of g: 3^4 +3 -1 =81 +2 = 83 or 2^4 +2 - 1 = 16 + 1 = 17. Both are odd and (-1) to the odd power results into (-1). Statement (2) provides that g is even and therefore an even integer - applying the logic from Statement (1) - Sufficient.
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ugimba wrote: What is the value of (-1)^{g^4 + g - 1} ?
1. g is an integer
2. g is even
D. Stmt1: We need to test with odd and even integers. odd integer: (-1)^{odd^4 + odd - 1} => (-1)^{odd}=-1even integer: (-1)^{even^4 + even - 1} => (-1)^{even}=-1Suff. Stmt2: As we have seen in Stmt 1, g=even integer results in -1. Suff
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if g = -1... (-1)^(1-1-1) = (-1)^(-1) = -1... so negative numbers result in -1 also making A sufficient.
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Oh, good question. I even got this one right! Just for fun, I raised the number to a negative power and came up with the same answer. For instance, if g=0, then -1 is raised to the negative first power (0+0-1). The reciprical of -1 is 1/-1, which still equals -1.
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I read the question incorrectly. I thought it was: (-1)^(g^4+g^(-1)). I didn't know to tackle it.
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so, g^4+g-1 is even for any integer g, am I right?
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No, odd:
1^4+1-1 = 1
2^4+2-1 = 17
-1^4-1-1 = -1
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mad tricky for statement 1
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Since we need to find the value of (-1) raise to something we just need to know wheteher the power is odd or even.
Statement one tells us its integer, but it can be odd or even. So we will get two value i.e -1 and 1.
Statement 2 tells us its an vene integer so we can clearly conclude what would be the value
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bb wrote: FYI - here is the latest official explanation (not updated yet in the tests database - we are editing them offline).
Let me know if you have any comments about quality I think the updated explanation is very clear. But when do you think these edits will be finished and updated in the test database? It sounds like a difficult and time consuming task. Good luck!
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A
Rephrase the question: is g^4 + g -1 odd or even? If we determine this then we can know for sure the value of the complete expression
S1: g is an integer -->
if g is odd then g^4 - g - 1= O + O - 1 = E - 1 = O
if g is even then g^4 - g - 1 = E + E -1 = E - 1 = O
this is true for special cases such as g = -1, 0, 1
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sleekmover wrote: A
Rephrase the question: is g^4 + g -1 odd or even? If we determine this then we can know for sure the value of the complete expression
S1: g is an integer -->
if g is odd then g^4 - g - 1= O + O - 1 = E - 1 = O
if g is even then g^4 - g - 1 = E + E -1 = E - 1 = O
this is true for special cases such as g = -1, 0, 1 Well I got excited and arrived at the answer too early. Obviously S2 also provides the answer as it says g is Even (a possibility that is considered already in explanation of S1) (Though this is kind of wierd question in which one solution is a subset of information provided the first solution) Correct ans: D
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ugimba wrote: What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer 2. g is even * 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient Source: GMAT Club Tests - hardest GMAT questions shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right? I actually got the concept tested on this question but didn't bother to test the variable G in statement 1) so I got it wrong selecting B  First the concept is testing the special case of -1 as a base along with the exponent (even or odd). If the exponent is an even number then the answer will be 1, but if the exponent is an odd number the answer will be -1 (because a negative base will take the same sign if the exponent is odd..in addition this is a special case of 1 so the value won't change and will be -1) Here is how I did it the 2nd time around. I chose the integers 2 and 3. -1^(2^4)+(2-1) -1^(even)+(odd) <---even + odd = odd so -1 will be raised to an odd power which will result in -1 as the answer -1^(3^4)+(3-1) -1^(odd)+(even) <-------odd + even = odd so -1 will be raised to an odd power which will result in -1 as the answer Statement 1) is sufficient For statement 2 if g is even then any number raised to an even integer such as 4 will yield EVEN. G-1 will equal ODD because an even - odd = odd We take the result of even + odd and we get ODD for the exponent -1^odd exponent will equal -1 SUFFICIENT
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