UPSC Prelims 2026 CSAT, question 29

Topic: Number system

Q29

Three variables $x,y$ and $z$ take values $2,3,4$ or $5$ such that their values are always distinct. If $M$ and $N$ denote the largest possible value and the smallest possible value, respectively, for the expression ${(x \times y)+z}$ ; then $M-N$ is

(a) 11
(b) 12
(c) 13Correct answer
(d) 14

Solution.

Answer: (c) 13

To maximize $(x \times y) + z$ for distinct $x, y, z \in \{2, 3, 4, 5\}$ , choose the two largest numbers for the product and the third largest for $z$ : $M = (5 \times 4) + 3 = 23$ .
To minimize $(x \times y) + z$ , choose the two smallest numbers for the product and the next smallest for $z$ : $N = (2 \times 3) + 4 = 10$ .
Therefore, $M - N = 23 - 10 = 13$ .