Grades 5-6 Video Solutions 2015-Level 5&6 Video Solutions 2015 problem24

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Question number 24. The number 100 is multiplied either by 2 or by 3. Then the result is increased  either by 1 or by 2. And then the new result is divided either by 3 or by 4. The final result is a natural number. What is this final result?  Well, let's follow the directions here and begin by multiplying 100 by 2 or by 3. So we have here, begin with 100, and we're going to multiply it by 2, or we're going to multiply  it by 3. And that will give us either 200 or 300. Then we have to increase the result by 1 or by 2. So plus 1 gives us 201. Plus 2 gives us 202. And with 300, we do the same.  Plus 1 gives us 301. Plus 2 gives us a 302. Now, the next part of the problem asks us to divide by either 3 or by 4. And the final result has to be a natural number. So our  numbers here have to be divisible by 3 or divisible by 4. Well, let's check which ones  are divisible by 3. Divisibility by 3, recall, is based on having a digit sum that is divisible  by 3. So 201 has a digit sum of 2 plus 0 plus 1, that is divisible by 3. So we can simply say  here that divided by 3 is equal to, that would be 67. 202 has a digit sum of 4, so that is not  divisible by 3. 301 has a digit sum of 4, that is not divisible by 3. And 302 has a digit sum of 5,  which is also not divisible by 3. So only 201 is divisible by 3. Now let's check divisibility by  4. That number would have to be even to begin with. And it's equivalent to saying we can divide  by 2 twice. So 202 divided by 2 is 101, which is odd. So we don't have divisibility by 4, we cannot divide by 2 twice. And 302 here divided by 2 would give us 151, which is also  odd. So the only number that we have found here that is divisible by 3 or by 4 is 201, with the quotient equal to 67. So that is that final result, the natural number we're looking  for. And this problem is 67. And that gives us answer C.

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