The edges of the cubical frame are made from plastic straws. How much longer is the total length of the plastic edges of a cube whose edges is 10cm compared to a cube whose edge is 8cm?

Question

16cm
32cm
24cm
8cm

In a Mathematics test, 35 students passed and 30% failed. How many students took the test?
60
40
30
50

Each bag of rice contains 50kg. what would be the increase in price if the cost of one bag of rice goes from P 950.00 to P 1,200.00?
P 250.00
P 7.50.00
P 3.75.00
P 5.00

How much greater is the sum of the first 20 counting numbers greater than the sum of the first 10 counting numbers?
55
155
100
110

Answer 1

Let's solve each problem step by step:

1. Total length of plastic edges of a cube:

   • The formula for the total edge length of a cube is \(12 \times\) (edge length).
   • For a cube with an edge of 10 cm: \[ 12 \times 10 = 120 \text{ cm} \]
   • For a cube with an edge of 8 cm: \[ 12 \times 8 = 96 \text{ cm} \]
   • The difference in total length: \[ 120 - 96 = 24 \text{ cm} \] So the answer is 24 cm.

2. Number of students who took the test:

   • If 30% failed, then 70% passed. Let \(x\) be the total number of students. Since 35 students passed: \[ 0.7x = 35 \]
   • Now solving for \(x\): \[ x = \frac{35}{0.7} = 50 \] Therefore, the answer is 50.

3. Increase in price of rice:

   • Initial price = P 950.00, Final price = P 1,200.00.
   • Increase in price: \[ 1,200 - 950 = P 250.00 \] So the answer is P 250.00.

4. Sum of the first 20 counting numbers vs. the first 10 counting numbers:

   • The sum of the first \(n\) counting numbers is given by the formula \(\frac{n(n + 1)}{2}\).
   • Sum of the first 20 counting numbers: \[ \frac{20(20 + 1)}{2} = \frac{20 \times 21}{2} = 210 \]
   • Sum of the first 10 counting numbers: \[ \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = 55 \]
   • The difference: \[ 210 - 55 = 155 \] Thus, the answer is 155.

In summary, the answers are:

1. 24 cm
2. 50
3. P 250.00
4. 155