Question 705004

SCQMEDIUM

In how many distinct ways can 128 identical marbles be arranged in a complete rectangular grid (disregarding the orientation of the grid)?

(A)

7

(B)

6

(C)

5

(D)

4

Detailed Solution

For a rectangular grid of 128 marbles, we need to find pairs of integers (m,n)(m, n) such that m×n=128m \times n = 128. The factor pairs of 128 are: (1,128),(2,64),(4,32),(8,16)(1, 128), (2, 64), (4, 32), (8, 16). There are 4 such distinct pairs.

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