Q9·CSAT · Prelims 2026
Optimization — Discrete Variable Bounds
NumericalPermutation & CombinationArithmetic Problem● Easy
Question
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 × y) + z\}; then M - N is
Options
a
11
b
12
cAnswer
13
d
14
Explanation
To solve for the range of the expression E = (x × y) + z using the distinct integers \{2, 3, 4, 5\}:
To maximize the expression (⟨MATH⟩M⟨/MATH⟩): Assign the largest available numbers to the multiplicative product, and the next largest to the additive component. Set x = 5 and y = 4 (or vice versa), and z = 3.
M = (5 × 4) + 3 = 20 + 3 = 23
To minimize the expression (⟨MATH⟩N⟨/MATH⟩): Assign the smallest available numbers to the multiplicative product, and the next smallest to the additive component. Set x = 2 and y = 3 (or vice versa), and z = 4.
N = (2 × 3) + 4 = 6 + 4 = 10
Calculate the Difference:
M - N = 23 - 10 = 13
To optimize an expression containing both multiplication and addition, assign the largest values to the multiplicative terms to maximize the output, and the smallest values to minimize it.
Answer: (c).
Question details
Year
2026
Paper
CSAT
Question
Q9
Section
Quantitative Aptitude
Sub-topic
Permutation & Combination
Type
Arithmetic Problem
Difficulty
Easy
Source hint
Standard optimization — algebraic extrema maximization
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