2016 New Spec

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AS Question 5

The algorithm, represented using pseudo-code in Figure 4, describes a method to calculate the additive or multiplicative persistence of a two-digit integer. The examples below illustrate how additive and multiplicative persistence are calculated.

Example: calculating the additive persistence of 87

8 + 7 = 15
1 + 5 = 6 

After 2 steps the method results in a one digit answer so the additive persistence of 87 is 2.

Example: calculating the multiplicative persistence of 39

3 * 9 = 27
2 * 7 = 14 
1 * 4 = 4 

After 3 steps the method results in a one digit answer so the multiplicative persistence of 39 is 3.

Figure 4

OUTPUT "Enter integer (0-99): "
INPUT Value
OUTPUT "Calculate additive or multiplicative persistence (a or m)? "
INPUT Operation
Count = 0
WHILE Value > 9

IF Operation = "a" THEN
Value = (Value DIV 10) + (Value MOD 10)
ELSE
Value = (Value DIV 10) * (Value MOD 10)
ENDIF
Count = Count + 1

ENDWHILE
OUTPUT "The persistence is: "
OUTPUT Count

The MOD operator calculates the remainder resulting from an integer division, for example, 10 MOD 3 = 1. The DIV operator calculates integer division, for example 10 DIV 3 = 3.

What you need to do

  1. Write a program for the algorithm in Figure 4.
  2. Test the program by showing the result of entering 47, followed by m when prompted by the program.
  3. Test the program by showing the result of entering 77, followed by a when prompted by the program.