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

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

1. \(g^2<1\)
2. \(g^2+2g\)

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient

“If g is an integer what is the value of \((-1)^{g^{4-1}}\)?”- is the topic of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements.GMAT data sufficiency comprise 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution:

From the statement (1), we have \(g^2<1\)

This statement tells that -1 < g < 1. Since, g is an integer then g = 0.

This would be sufficient to calculate the value of \((-1)^{g{^4-1}}\)

Now consider the statement (2), we have \(g^2+2g\) Put this statement equal to 0.

As this is a Quadratic equation, we will have two roots of the equation.

Taking ‘g’ common for this equation,\(g^2+2g\) = 0

g (g + 2) = 0

Either g = 0

OR

g + 2 = 0, that means g = -2

As both the values of g are even then = \((-1){^{even^{4}-1}} = (-1)^{even-1}= (-1)^{odd}=-1\)

Hence, this is sufficient.

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