Electronic Graduate Management Admission Test (e-GMAT) Practice Exam

To determine the appropriate value of \( n^2 \) in relation to its factors when \( n^3 \) is divisible by 2500, we begin by examining the prime factorization of 2500.

2500 can be expressed as:

\[

2500 = 25 \times 100 = 5^2 \times (10^2) = 5^2 \times (2 \times 5)^2 = 5^2 \times 2^2 \times 5^2 = 2^2 \times 5^4

\]

Thus, the prime factorization of 2500 is:

\[

2500 = 2^2 \times 5^4

\]

Next, since \( n^3 \) is divisible by \( 2500 \), it follows that:

\[

n^3 = k \cdot (2^2 \times 5^4)

\]

for some integer \( k \). For \( n^3 \) to contain the factors \( 2^2 \) and \( 5^4 \), we can deduce how many times \( n \) must contain the factors 2 and 5.

Let