Graphics Interpretation - Other Chart Types

The flow chart describes the process by which the Collatz conjecture can be tested. The Collatz conjecture states that no matter what natural number you pick, if you follow the process, you will eventually reach 1.

From each drop-down menu, select the option that creates the most accurate statement based on the information provided.

If you are at the decision point "Even?" and you have an even number, the next step is to [[dropdown1]] .

If you start by picking the number 5, then you will have to divide by 2 a total of [[dropdown2]] times before stopping.

Incorrect.

The decision point "Even?" has an arrow labeled "No" that leads to "Multiply by 3 and then add 1." This means that you should only perform this step if the number is not even.

Incorrect.

You should progress through the flow chart from left to right. In this flow chart, the step labeled "Pick a number" is the leftmost step. Therefore, it is the first step that you should perform.

To determine what to do with an even number, look at the decision point labeled "Even?" Identify the step that you should perform when the answer is "Yes."

Right!

The decision point "Even?" has an arrow labeled "Yes" that leads to "Divide by 2." Thus, you should divide the number by 2 if it is even.

Incorrect.

You may have miscounted the number of times you divided by 2 or made a calculation error. Remember to keep track as you go through the flow chart from left to right.

Start with the leftmost step "Pick a number" and choose the number 5. Then follow the arrows to the next step, represented by rectangles, or decision point, represented by diamonds. At each decision point, you should follow the arrow-"Yes" or "No"-that answers the question for the number you are currently working with.

That's right! Start with the leftmost step, "Pick a number," and choose the number 5. Then proceed to the next decision point "Even?" Since 5 is not even, follow the "No" arrow. This leads to "Multiply by 3 and then add 1," so you get $$3 \cdot 5 + 1 = 16$$. Proceeding to "Equal to 1?" you get a "No" answer, so you should follow the "No" arrow back to "Even?" Continue the process in the same way: 16 is even, so divide it by 2. The result is $$16 \div 2 = 8$$. This number is not 1. But it is even, so divide by 2 again to get $$8 \div 2 = 4$$. Again, your number is not 1 but it is even, so divide by 2 again: $$4 \div 2 = 2$$. Same thing, it's not 1, but it is even. Divide by 2 to get $$2 \div 2 = 1$$. Finally, the result is 1, so you should stop. Notice that you divided by 2 a total of four times. Alternatively, you might have noticed that $$16 = 2^4$$. This means that if you divide 16 by 2 four times you will end up with 1.

Incorrect.

You might have miscounted the number of times you divided or made a calculation error when following the process. Keep a running tally as you go through the flow chart from left to right.

Start with the leftmost step "Pick a number" and choose the number 5. Then follow the arrows to the next step, represented by rectangles, or decision point, represented by diamonds. At each decision point, you should follow the arrow-"Yes" or "No"-that answers the question for the number you are currently working with.

Incorrect.

You might have miscounted the number of times you divided or made a calculation error when following the process. Make sure you keep a running tally of the number of times you divided by 2 as you go through the flow chart from left to right.

Start with the leftmost step "Pick a number" and choose the number 5. Then follow the arrows to the next step, represented by rectangles, or decision point represented by diamonds. At each decision point, you should follow the arrow-"Yes" or "No"-that answers the question for the number you are currently working with.

divide it by 2

pick a number

multiply it by 3 and then add 1

2

3

4

5