Multiple choice

The number of employees who work at Company $A$ increased by $18\%$ during the year $2003$. During $2004$, the number of employees increased by $26\%$. Calculate the approximate percent of the increase, to the nearest percent, in employment over the two-year period.

  1. $31\%$
  2. $44\%$
  3. $49\%$
  4. $53\%$
  5. $65\%$
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C Correct answer
Explanation

Let the initial number of employees be 100. After 2003, it becomes 100 * 1.18 = 118. After 2004, it becomes 118 * 1.26 = 148.68. The total increase is 48.68%, which rounds to 49%.

AI explanation

Using the successive percentage change formula of X + Y + (XY)/100, we substitute the respective percentage increases of 18 and 26. The calculation is 18 + 26 + (18 * 26)/100, which equals 44 + 4.68, resulting in a net increase of 48.68%. Rounding this to the nearest whole percent gives an approximate 49% increase in employment over the two-year period.

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