Problem 6

Explanation

We need to determine the sales pattern for each item to predict the sales volume in 2016.

Pattern Analysis

1. Shirts: Sales data is $50, 35, 20, 70, 55$.

   • The pattern shows a consistent decrease of $15$ ($50 \xrightarrow{-15} 35 \xrightarrow{-15} 20$ and $70 \xrightarrow{-15} 55$).
   • Prediction for 2016: $55 - 15 = 40$.

2. Pants: Sales data is $60, 60, 50, 40, 40$.

   • The changes are $0, -10, -10, 0$.
   • The pattern repeats the cycle of "constant, decrease, decrease". Following this, the next change is a decrease of $10$.
   • Prediction for 2016: $40 - 10 = 30$.

3. Suits: Sales data is $40, 55, 45, 60, 50$.

   • The changes are $+15, -10, +15, -10$.
   • The pattern alternates between adding $15$ and subtracting $10$. The next step is adding $15$.
   • Prediction for 2016: $50 + 15 = 65$.

Evaluating the Options

Using the predictions (Shirts = $40$, Pants = $30$, Suits = $65$):

1. Pants sales are 10 fewer than shirts: $30 = 40 - 10$ (Correct).
2. Suits sales are 35 more than pants: $65 = 30 + 35$ (Correct).
3. The total sales of shirts and pants is less than 70: $40 + 30 = 70$. Since $70$ is not less than $70$, this statement is incorrect.
4. Shirts sales are 10 more than pants: $40 = 30 + 10$ (Correct).
5. Pants sales are 35 less than suits: $30 = 65 - 35$ (Correct).

The question asks for the incorrect prediction. Therefore, the answer is The total sales of shirts and pants is less than 70.