CAT 2024 Number System Question (Medium)

Question

If and are natural numbers such that , and , then equals

Accepted Answer

Step 1 Express in terms of prime factors Suppose Then We are told 2 an cdot 3 bn 2 25 cdot 3 40 Rightarrow an 25, quad bn 40 --- Step 2 Solve for and From , , and Let s find common divisors of 25 and 40 - Common divisors of 25 1, 5, 25 - Common divisors of 40 1, 2, 4, 5, 8, 10, 20, 40 So possible va

CAT 2024

Quantitative

Number System

Medium

If $m$ and $n$ are natural numbers such that $n>1$ , and $m^n=2^{25} \times 3^{40}$ , then $m-n$ equals

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