Number Line Problem

Number Theory Level 1

The image above represents the number line. Which is the possible value at which point A A can lie?

Note: The actual distance of the points is not considered in this problem.

4 5 \dfrac 45 13 49 \dfrac{13}{49} 7 10 \dfrac{7}{10} None of the given choices

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Pham Khanh
Aug 18, 2016

We saw that all the choices are greater than 0. We got 3 5 > 1 2 > 13 49 \frac{3}{5}~>~\frac{1}{2}~>~\frac{13}{49} but 3 5 < 4 5 (obviously) \frac{3}{5}~<~\frac{4}{5}~\text{(obviously)} and 3 5 = 3 × 2 5 × 2 = 6 10 < 7 10 \frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}~<~\frac{7}{10} So the answer is 13 49 \Large \boxed{\frac{13}{49}}

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Loo Soo Yong
Sep 18, 2016

Another way is to perform a division and change them into decimal places.

3/5 = 0.6 13/49 is approximately equal to 0.265 4/5 = 0.8 7/10 = 0.7

Clearly - the only solution is 13/49.

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