Question

Given \( A = x + y^2 + z^3 \). If x increases by 6300%, y increases by 700% and z increases by 300%, then what is the percentage increase in the value of A?

• A. 1200%
• B. 1800%
• C. 2600%
• D. 6300%

Hint:

Turn each percentage rise into a multiplying factor and see how each term of A scales when combined.

Answer 1

The Correct Option is D

Step 1: Convert each percentage rise into a multiplying factor.
An increase of 6300% means the new value is \( 1 + 63 = 64 \) times the old value, so new \( x = 64x \).
An increase of 700% means the new value is \( 1 + 7 = 8 \) times the old value, so new \( y = 8y \).
An increase of 300% means the new value is \( 1 + 3 = 4 \) times the old value, so new \( z = 4z \).

Step 2: Apply these factors to each term of A.
The new x term is \( 64x \).
The new y term is \( (8y)^2 = 64y^2 \).
The new z term is \( (4z)^3 = 64z^3 \).

Step 3: Add the new terms and compare with the old A.
New \( A = 64x + 64y^2 + 64z^3 = 64(x+y^2+z^3) = 64A \).
So the new value of A is exactly 64 times the old value of A.

Step 4: Find the percentage increase.
Percentage increase \( = \frac{64A - A}{A} \times 100 = 63 \times 100 = 6300\% \).

Final Answer:
Every term of A scales by exactly 64, so A itself increases by 6300 percent. \[ \boxed{6300\%} \]