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# 2017 MMC National Finals Grade 6 Individual Competition 60-second Questions

1. A cube of side 4 dm is made up of individual 1 dm cubes. How many of the 1 dm cubes have exactly two faces exposed?
[Sol]

The cubes that have exactly 2 faces exposed are the cubes on the edges but not on the corners. We have

$12$ edges $\times 2$ cubes per edge $= \boxed{24}$

2. Risa took her periodical tests on several subjects. Her average score not including her Mathematics score is 87. Her average score including her Mathematics score is 86. If her score in Mathematics is 82, how many periodical tests did she take including that in Mathematics?

[Sol]

Sum of all scores = Sum of scores without mathematics + score in mathematics
If we let $n =$ number of tests

$86 \times n = 87 \times (n - 1) + 82$

$n = \boxed{5}$

3.  A car is travelling at an average speed of 63 kilometers per hour. What is its speed in meters per second?

[Sol]

$63 \dfrac{\mathrm{km}}{\mathrm{hr}} \times \dfrac{1000 \, \mathrm{m}}{ 1 \mathrm{km}} \times \dfrac{1 \, \mathrm{hr}}{3600 \mathrm{s}} = 63 \times \dfrac{5}{18} \dfrac{\mathrm{m}}{\mathrm{s}} = \boxed{17.5 \, \mathrm{m}/\mathrm{s}}$

4.  The sum of the minuend, the subtrahend, and difference of a subtraction sentence is 106. If the difference is greater than the subtrahend by 29, what is the subtrahend in the subtraction sentence?

[Sol]

Letting $s =$ subtrahend, we have $s+ 29 =$ difference, and from the first sentence, we have
$106 - (s) - (s + 29) = 77 - 2s =$ minuend.

Since, in a subtraction sentence, we have minuend – subtrahend = difference,
$(77 - 2s) - (s) = (s + 29)$
$s =$  subtrahend $= \boxed{12}$

5.  Find the values of A, B, C, and D to make the subtraction sentence TRUE: $\overline{A42D} - \overline{4BC4} = 4444$

[Sol]

Considering the last digits, $D - 4 = 4$ so we have $D = 8$
Tens digits: $2 - C = 4$. Obviously, it borrows a 10 from the 4 in $\overline{A42D}$.
So $12 - C = 4$ gives $C = 8$.
Hundreds digits: Instead of  $4 - B$, we take $3 - B = 4$ from the borrowing in the ten’s.
Again, it borrows a 10 from A, $13 - B = 4$ gives $B = 9$.
Thousands digits: $(A - 1) - 4 = 4 \rightarrow A = 9$.

In summary, $\boxed{A = B = 9, C = D = 8}$