Maths Olympiad Prep

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, 2012

Algebra Difficulty 1.2 Junior Find the answer Canada

Which of the following statements is true?

\text{}0islessthan is less than -5{}
\text{}7islessthan is less than -1{}
10 is less than\text{10 is less than}14\frac{1}{4}{}
\text{}-1islessthan is less than -3{}
\text{}-8islessthan is less than -2{}

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

Solution

Consider placing each of the two numbers from each answer on a number line.

Numbers decrease in value as we move to the left along a number line.

Since the first number listed in the pair must be less than the second, we want the first number to be to the left of the second number on the number line.
The five possible answers are each given on the number lines shown.

[[IMAGE0]]

Hide/Reveal Description of Number Lines

In the first number line, the numbers placed, from left to right, are 5-5 and 00.
In the second number line, the numbers placed, from left to right, are 1-1, 00 and 77.
In the third number line, the numbers placed, from left to right, are 00, 14\frac{1}{4} and 1010.
In the fourth number line, the numbers placed, from left to right, are 3-3, 1-1 and 00.
In the fifth number line, the numbers placed, from left to right, are 8-8, 2-2 and 00.

The last number line is the only one for which the first number listed (8-8) is positioned to the left of (is less than) the second number (2-2).

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