CAT 2022 Number System Question (Hard)

Question

For natural numbers , , and , if and , then what is the minimum possible value of ?

Accepted Answer

Step 1 Subtract the Equations Subtract Eq. 1 from Eq. 2 xz yz - xy yz 51 - 19 xz - xy 32 Factor out x z - y 32 Since , , are natural numbers, must be a divisor of 32. Divisors of 32 are 1, 2, 4, 8, 16, 32 --- Step 2 Express in terms of z - y x quad Rightarrow quad z y x Substitute into Eq. 1 xy y y

CAT 2022

Quantitative

Number System

Hard

For natural numbers $x$ , $y$ , and $z$ , if $xy + yz = 19$ and $yz + xz = 51$ , then what is the minimum possible value of $xyz$ ?

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