Maths Olympiad Prep

Track / Stage 1 / 14 of 240 #14 of 2444

Problem 14

Number theory Difficulty 1.1 Find the answer CEMC Fermat · Canada · 2014

The integer 2014 is between

(A) 10 0 and 10 1\text{10 0 and 10 1} (B) 10 1 and 10 2\text{10 1 and 10 2} (C) 10 2 and 10 3\text{10 2 and 10 3} (D) 10 3 and 10 4\text{10 3 and 10 4} (E) 10 4 and 10 5\text{10 4 and 10 5}

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Next problem →

Official solution

Since 100=110^0=1, 101=1010^1=10, 102=10010^2=100, 103=100010^3=1000, 104=10 00010^4 = 10\,000, and 105=100 00010^5 = 100\,000, then 2014 is between 10310^3 and 10410^4.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.