School Olympiads - International Mathematics Olympiad (IMO)

Number Theory, Advanced Algebra & Olympiad Geometry question bank (Mathematical Reasoning & Achievers Section)

Practice 51 free School Olympiads - International Mathematics Olympiad (IMO) Mathematical Reasoning & Achievers Section - Number Theory, Advanced Algebra & Olympiad Geometry questions with answers and step-by-step solutions.

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Q1.

Achievers Section (Cryptarithms): In the classic cryptarithmic addition in 'Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms' where each distinct letter represents a unique digit ($0-9$): $\text{SEND} + \text{MORE} = \text{MONEY}$. What is the value of the letter $M$ and $O$?

(A)

$M = 1$ and $O = 0$ (Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms)

(B)

$M = 2$ and $O = 1$

(C)

$M = 1$ and $O = 9$

(D)

$M = 9$ and $O = 0$

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Q2.

HOTS Challenge: How many positive integer factors does the number $N = 2^4 \times 3^3 \times 5^2$ have in 'Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms'?

(A)

60 factors ($(4+1)(3+1)(2+1) = 5 \times 4 \times 3 = 60$) (Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms)

(B)

24 factors

(C)

48 factors

(D)

120 factors

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