Question

owen follows the rule \divide by 2\ to write the pattern below. he will write two more numbers to complete the pattern. which statement is true?
800, 400, 200, 100, □, □
every number in the pattern will have a 0 in its ones place.
every number in the pattern will have a 0 or a 5 in its ones place.

Explanation:

Step1: Find next numbers

The rule is "divide by 2". Start with 100: \(100\div2 = 50\), then \(50\div2 = 25\).

Step2: Check ones place

First number in pattern: 800 (ones place 0), 400 (0), 200 (0), 100 (0), 50 (0? No, 50 has 0? Wait, 50 ones place is 0? Wait, 50: ones digit 0? No, 50's ones place is 0? Wait, no: 50 is 5 tens and 0 ones. Then 25: ones place 5. Wait, initial numbers: 800 (0), 400 (0), 200 (0), 100 (0). Then next: 50 (0), 25 (5). Wait, the first statement: "Every number in the pattern will have a 0 in its ones place." But 25 has 5, so that's false. Second statement: "Every number in the pattern will have a 0 or a 5 in its ones place." Let's check: 800 (0), 400 (0), 200 (0), 100 (0), 50 (0), 25 (5). All have 0 or 5 in ones place. Wait, but wait, the first four numbers have 0, then 50 (0), 25 (5). Wait, maybe I miscalculated. Wait, the pattern is 800, 400, 200, 100, then next is 100÷2=50, then 50÷2=25. So the numbers are 800, 400, 200, 100, 50, 25. Now check ones place: 800 (0), 400 (0), 200 (0), 100 (0), 50 (0), 25 (5). So the second statement: "Every number in the pattern will have a 0 or a 5 in its ones place." is true. Wait, but the first option: "Every number in the pattern will have a 0 in its ones place." is false because 25 has 5. So the correct statement is the second one. Wait, but let's re-express. Wait, the two statements:

1. Every number in the pattern will have a 0 in its ones place.

1. Every number in the pattern will have a 0 or a 5 in its ones place.

Let's list all numbers: 800 (0), 400 (0), 200 (0), 100 (0), 50 (0), 25 (5). So for statement 1: 25 has 5, so false. Statement 2: all have 0 or 5, so true. Wait, but maybe the problem is that Owen will write two more numbers. So the pattern as given is 800, 400, 200, 100, and he writes two more: 50 and 25. So the numbers are 800, 400, 200, 100, 50, 25. Now check the ones place:

• 800: 0

• 400: 0

• 200: 0

• 100: 0

• 50: 0

• 25: 5

So statement 1: "Every number... 0 in ones place" is false (25 has 5). Statement 2: "Every number... 0 or 5 in ones place" is true (all have 0 or 5). Wait, but maybe I made a mistake. Wait, 50's ones place is 0, 25's is 5. So yes, 0 or 5. So the second statement is true.

Answer:

The statement "Every number in the pattern will have a 0 or a 5 in its ones place" is true. (Assuming the options are labeled, e.g., if the second option is "Every number in the pattern will have a 0 or a 5 in its ones place", then the answer is that option.)