1998 AHSME Problems/Problem 5

Problem 5

If $2^{1998}-2^{1997}-2^{1996}+2^{1995} = k \cdot 2^{1995},$ what is the value of $k$ ?

$\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 4 \qquad \mathrm{(E) \ } 5$

$2^{1998} - 2^{1997} - 2^{1996} = 2^{1996}$ . $2^{1996} + 2^{1995} = 2^{1995}(2 + 1) = 3 \cdot 2^{1995}$ . So, the answer is $\text{(C)}.$

1998 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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