On Henry's smartphone, the diagram shows how much time he spent last week on each of his apps. The apps are ordered from the most to the least time spent. This week, he spent exactly the same amount of time as last week on two of his apps, but only half as much time on the other two. Which of the diagrams below cannot be the diagram for this week? Last week, we see that he spent three hours, two hours, two hours, and one hour on his four apps. So, to get the possibilities for this week, we just need to pick two of these times and divide them by two, and leave the other two times the same. So, we can either divide these guys, these two by two, to get three, two, one, one-half, or we can divide these two by two to get three, one, one, one. We could cut these ones in half to get three halves, one, two, one, or we could cut the first and the last in half to get three halves, two, two, one-half. Now we just have to look through all the possibilities. This one is three, one, one, one, and that's one of our options. This one is two, two, three halves, one-half, which is another one of our options. This one is two, three halves, one, one, which is this option. This one is three, two, one, one-half, which is the first option. And this one is three, two, two, one-half. The three, two, and two are repeating three times instead of repeating two times. So that has to be the one that's impossible, so our answer is E.

app usage

time distribution

impossible combination

Henry

time halving