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If m=-1 and n = 1^2 + 2^2 + … + 10^2, what is the value of

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If m=-1 and n = 1^2 + 2^2 + … + 10^2, what is the value of

by Max@Math Revolution » Sun Jul 29, 2018 11:55 pm

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[Math Revolution GMAT math practice question]

If m=-1 and n = 1^2 + 2^2 + ... + 10^2, what is the value of m^n+m^{n+1}+m^{n+2}+m^{n+3}?

A. -2
B. -1
C. 0
D. 1
E. 2
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by GMATGuruNY » Mon Jul 30, 2018 2:06 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If m=-1 and n = 1^2 + 2^2 + ... + 10^2, what is the value of m^n+m^{n+1}+m^{n+2}+m^{n+3}?

A. -2
B. -1
C. 0
D. 1
E. 2
(-1)^odd = -1.
(-1)^even = 1.
The exponents for the expression in blue are 4 consecutive integers -- n, n+1, n+2, n+3 -- implying that two of the exponents will be ODD, while the other two will be EVEN.
Thus, two of the terms in the blue expression must be equal to -1, while the other two must be equal to 1:
-1 + -1 + 1 + 1 = 0.

The correct answer is C.
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by Max@Math Revolution » Wed Aug 01, 2018 12:54 am
=>

m^n+m^{n+1}+m^{n+2}+m^{n+3}
= m^n(1+m^1+m^2+m^3)
= (-1)^n(1+(-1)^1+(-1)^2+(-1)^3)
= (-1)^n* 0 = 0
Whatever the value of n is, the answer is 0.

Therefore, C is the answer.

Answer: C
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by deloitte247 » Sat Aug 04, 2018 6:16 am
What is the value of
$$m^n\ +\ m^{\left(n\ +\ 1\right)}\ +\ m^{\left(n\ +\ 3\right)}$$
$$m^n\ +\ \left(1\ +\ m^1\ +\ m^{^2}\ +\ m^3\right)$$
$$-1^n\ \left(1\ +\ \left(-1\right)^1\ +\ \left(-1\right)^2\ +\ \left(-1\right)^3\right)$$
$$-1^n\ \left(1\ +\ \left(-1\right)\ +\ \left(1\right)\ +\left(-1\right)\right)$$
$$-1^n\ \left(0\right)$$
$$-1^n\ \cdot\ 0\ =\ 0$$
Option C is the correct answer.
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