Question

xander, yves, and zeke are all reading the same book. the time it takes each student to read the book is listed in the table below.

student	time, in minutes
yves	$60 \times \frac{5}{3}$
zeke	$60 \times \frac{3}{3}$

which of the following statements is true?
\\(\bigcirc\\) a. xander takes less than 60 minutes to read the book since \\(\frac{3}{5}\\) is less than 1.
\\(\bigcirc\\) b. xander takes more time to read the book than zeke since \\(\frac{3}{5}\\) is greater than \\(\frac{3}{3}\\)
\\(\bigcirc\\) c. yves takes less than 60 minutes to read the book since \\(\frac{5}{3}\\) is less than 1.
\\(\bigcirc\\) d. zeke takes 180 minutes to read the book since $60 \times 3 = 180$.

Explanation:

• For Option A: When a number (60 here) is multiplied by a fraction less than 1 ($\frac{3}{5}<1$), the result is less than the original number. So $60\times\frac{3}{5}=36$, which is less than 60. This statement is correct.
• For Option B: $\frac{3}{5} = 0.6$ and $\frac{3}{3}=1$, so $\frac{3}{5}<\frac{3}{3}$. Then $60\times\frac{3}{5}=36$ and $60\times\frac{3}{3}=60$, so Xander takes less time than Zeke. This statement is wrong.
• For Option C: $\frac{5}{3}\approx1.67>1$, so when 60 is multiplied by $\frac{5}{3}$, $60\times\frac{5}{3} = 100$, which is more than 60. This statement is wrong.
• For Option D: $60\times\frac{3}{3}=60\times1 = 60$, not 180. This statement is wrong.

Answer:

A. Xander takes less than 60 minutes to read the book since $\frac{3}{5}$ is less than 1.