For any positive three-digit integer n, the function f is defined as $f(n) = 2^x3^y5^z$ , where x, y, and z represent the hundreds, tens, and units digits of n, respectively.

Given that m and v are three-digit positive integers satisfying $f(m)=9*f(v)$ , what is the value of $m-v=$ ?

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Official Explanation

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f(m) = 9 \cdot f(v)

Substituting the prime factorizations:

2^a \cdot 3^b \cdot 5^c = 9 \cdot 2^d \cdot 3^e \cdot 5^f

Thus,

m and v share the same hundreds and units digits, but m’s tens digit exceeds v’s by 2. The numerical difference is:…

Comments

AkhilFeb 1, 2025

Checked question.

KaustavApr 10, 2025

thank you for sharing

TafreeJul 13, 2024

taking my GMAT next month, this helps!

What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).