GRE® Quant Practice Q10

This GRE maths sample question is a Numeric Entry question in Number Properties. Concept tested: Rules of Exponents.

Question 10: If (3^-22 + 3^-19 + 3^-17 + 3^-16) = k(3^-24), what is k?

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Video Explanation

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Explanatory Answer | GRE Problem Solving Question 10

Given: (3^-22 + 3^-19 + 3^-17 + 3^-16) = k(3^-24)
Taking 3^-22 common from both sides,
3^-22(1 + 3³ + 3⁵ + 3⁶) = k(3^-22(3^-2))

Divide both sides of the equation by 3^-22
1 + 3³ + 3⁵ + 3⁶ = k(3^-2)
1 + 27 + 243 + 729 = k(3^-2)
1000 = k(3^-2)

Multiply both sides of the equation by 3(²)
3² × 1000 = k
→ k = 9000.

9000 is the correct answer.