Wiley Edge Number System Quiz-4

Let the number be w.
The equation is 7w - 9 = 2w - 3.
Solving it, we get w = 6.

Let the number be c. The equation is 3c + 10 = 2c + 7. Solving it, we get c = 2.

To find the largest integer that divides all three numbers without leaving a remainder, we need to find the greatest common divisor (GCD) of the numbers. By calculating the GCD of 540, 630, and 810, we find that the largest integer that divides all three numbers is 18.

By calculating the GCD of 720, 900, and 1260, we find that the largest integer that divides all three numbers is 90.

By calculating the GCD of 480, 600, and 720, we find that the largest integer that divides all three numbers is 60.

The prime factorization of 72 is 2^3 * 3^2. To find the highest power of 72 that can divide 100!, we need to determine the number of factors of 2^3 and 3^2 in 100!.
The highest power of 2 in 100! is 97, and the highest power of 3 is 48.
Therefore, the highest power of 72 that can divide 100! is limited by the power of 3, which is 48.
Therefore, the answer is 6.

The prime factorization of 24 is 2^3 * 3.
The highest power of 2 in 90! is 87, and the highest power of 3 is 29. Therefore, the highest power of 24 that can divide 90! is limited by the power of 3, which is 29.
Therefore, the answer is 5.

Let's assume the first even number is x. The sum of the consecutive even numbers can be expressed as x + (x+2) + (x+4) + (x+6) + (x+8). Since there are 5 even numbers, the sum is 5x + 20.

The sum of 4 consecutive odd numbers can be expressed as y + (y+2) + (y+4) + (y+6).

Since there are 4 odd numbers, the sum is 4y + 12.

According to the question, 5x + 20 = 200.

Solving this equation gives x = 36.

Substituting x = 36 into the sum of odd numbers equation gives 4y + 12 = 116. Solving for y, we find y = 26.

Therefore, the sum of the 4 consecutive odd numbers is 4y + 12 = 4(26) + 12 = 104 + 12 = 116.

Let's assume the first odd number is x. The sum of the consecutive odd numbers can be expressed as x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) + (x+12) + (x+14).
Since there are 8 odd numbers, the sum is 8x + 56. The sum of 7 consecutive even numbers can be expressed as y + (y+2) + (y+4) + (y+6) + (y+8) + (y+10) + (y+12).
Since there are 7 even numbers, the sum is 7y + 42. According to the question, 8x + 56 = 425.
Solving this equation gives x = 41.
Substituting x = 41 into the sum of even numbers equation gives 7y + 42 = 425.
Solving for y, we find y = 59.
Therefore, the sum of the 7 consecutive even numbers is 7y + 42 = 7(59) + 42 = 413 + 42 = 455.

Let the numbers be y and (240 - y).
The equation becomes: (3/4)y - (2/3)(240 - y) = 20.
Solving this equation gives y = 70.