Grades 9-10 Video Solutions 2022-2022_9-10

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Question 28. The positive integer n is such that the product of its digits is 20. Which of the following could not be the product of the digits n plus 1? To  start this problem, let's take 20 and break it down by all the ways that it can be multiplied. So we can do 1 times 20, 2 times 10, 4 times 5, and 10 can be  broken into 2 and 5. Now since we're looking at digits, you can get rid of 20 and we can get rid of 10, but it breaks down into 2 and 5, but we already have 2  and 5. So we look at 1, 2, 4, and 5. So with these digits, you want to make a positive integer n that its products of the digits is 20, and then if we add 1,  we want to see these different solutions. So let's look at 40. If we break down 40, it can be broken down into 5 and 8, and 8 can be broken down into 3 twos. So to  get 40, we could have 5,222. The product of its digits is 40. If we subtract 1, then the product of its digits is 20, so it cannot be A. Next, we try 30. It can be  broken down into 5 and 6, and 6 into 3 and 2. So we could make a number 523 where the product of its digits is 30, and then one less, 522. The product of  the digits is 20, so it won't be B. If we start on the other end, 24, it's broken down into 4 and 6, and we can just write the number 46. The product of its  digits is 24, and one less, 45. The product is 20, so it won't be E. Next, we look at 25,  and we get 5 and 5. 55 will give us the product of 25, and one less, 54 gives us a product of 20,  so it can't be C. We are left with 35. 35 is broken down into 5 and 7. Unfortunately, we can't do much with this, so the answer is D, 35.

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