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If a, b, c and d are four consecutive integers (not necessar

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by Brent@GMATPrepNow » Tue Oct 01, 2019 11:36 am
If a, b, c and d are four consecutive integers (not necessarily in that order), and a^b = c^d, what is the LEAST possible value of a+b+c+d?

A) -8
B) -6
C) -2
D) 6
E) 12

Answer: B
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by deloitte247 » Sat Oct 12, 2019 8:29 am
$$1^n=1\ when\ n=any\ integer$$
$$-1^n=1\ when\ n=any\ even\ integer$$
$$n^0=1\ when\ n=any\ integer$$
If a=-1, b=-2, c=-3 and d=0
Following the expression
$$a^b=c^d$$
$$Therefore,\ \left(-1\right)^{-2}=-3^0$$
$$\frac{1}{\left(-1\right)^2}=1$$
$$\frac{1}{1}=1$$
This satisfies the given expression. So, the sum of the four integers = (-1) + (-2) + (-3) + (0) = -6

Answer = Option B
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