# GRE® Quant Practice Q10

#### Number Properties | Numeric Entry | Rules of Exponents

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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### 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.

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