ACT (Enhanced)MathematicsHard
A civil engineer is calculating the stress on a beam. The formula for the stress (S) is S = F/A, where F is the force applied and A is the cross-sectional area. If the force F is increased by 20% and the cross-sectional area A is decreased by 10%, what is the new stress in terms of the original stress S?
- A1.10 S
- B1.44 S
- C1.33 S
- D1.22 S
Show answer & explanationAnswer & explanation
Correct answer: C. 1.33 S
Original stress S = F/A. New force F' = 1.20F. New area A' = 0.90A. New stress S' = F'/A' = (1.20F) / (0.90A) = (1.20/0.90) * (F/A). Since F/A = S, S' = (1.20/0.90) * S = (12/9) * S = (4/3) * S ≈ 1.333 S.
Why the other options are wrong
- A. Incorrect calculation, perhaps only considering one change or incorrect division.
- B. Incorrect calculation, possibly by squaring 1.20 or similar error.
- D. Incorrect calculation, possibly by multiplying 1.20 by 0.90 or 1.10.
Percentage Change Application
To apply a percentage increase, multiply by (1 + percentage as decimal). To apply a percentage decrease, multiply by (1 - percentage as decimal).
- Increase by X% means multiply by (1 + X/100).
- Decrease by Y% means multiply by (1 - Y/100).
- Order of operations is important when combined with other calculations.
Memory trick: Percentages are like multipliers, changing numbers up or down.