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# 2017 MMC National Finals Grade 6 Individual Competition 30-second Questions

1. Arrange the following numbers from smallest to largest: $\dfrac{1}{2}, \dfrac{1}{3}, 0.33, 0.25, 0.2, \dfrac{5}{6}$.

[Sol]

Converting the fractions to decimals up to 4 places, 0.5, 0.3333, 0.33, 0.25, 0.2, 0.8333, and rearranging, $\boxed{0.2, 0.25, 0.33, \dfrac{1}{3}, \dfrac{1}{2}, \dfrac{5}{6}}$.

2. Two trains leave the same city at the same time traveling to opposite directions. One is traveling at an average speed of 65 km per hour and the other is travelling at an average speed of 75 km per hour. In how many hours will they be 350 km apart?

[Sol]

Since they leave the station at opposite directions,$65t + 75t = 350$
$t = 2.5$
Thus, $\boxed{2.5 \, hr}$

3. What is the product of $1\dfrac{1}{4} \times 1\dfrac{1}{5} \times 1\dfrac{1}{6} \times \cdots \times 1\dfrac{1}{99} \times 1\dfrac{1}{100}$ ?

[Sol]

4. A number is multiplied by 3 and then, the product is added to 2. The sum is then subtracted from 8. If the final result is -9, what is the number?

[Sol]

If $n$ is the number,

5. A block of wood with dimensions 24 cm by 32 cm by 64 cm is to be cut to form cubes. How many cubes of the same size with the longest possible length can be cut from the block so that no wood is wasted?

[Sol]

GCF(24, 32, 64) = 8. So the longest possible length of a cube is 8 cm. Therefore, 24/8 = 3, 32/8 = 4, 64/8 = 8. So there are $3 \times 4 \times 8 = \boxed{96}$.