将变量转换为数字，第二部分

这是两个关于将变量转换为数字的第两个，如果您确定您真正了解基础知识并准备使用这一集，则应启动这个。首先让我们开始回顾最后一集的内容。将变量转换为数字有三个常规步骤，首先将数字分配给变量，然后根据您解决问题的数字，最后，您可以在答案选择和您找到的答案之间查找匹配。现在我们将增加两个皱纹来将变量转换为数字。首先，如果答案选择包括我们到目前为止未见的变量，我们迄今为止我们只看到了有数字的答案选择，那么您也将将这些变量转换为数字。其次，如果多个答案选择工作然后您将需要返回，更改您的号码并再次通过此过程，直到您只有一个继续工作的答案选择。让我们在使用一些例子的更多详细信息中查看所有这些。
所以在这里，我们有一个例子是第一个新的原则，有时你必须把答案的变量转化为数字，但我们仍然会通过相同的三个基本步骤，所以让我们这样做。让我们开始阅读问题现在，'如果a，b和c是大于ab = 15和bc = 33的整数，则以下哪个必须是真的？'因此，第一步是选择工作的数字并记住您必须满足问题的所有限制所以请仔细选择。现在你可能自然地说过，如果次b是15，那么我们会为b的一个和五个来试试三个。但是让这个棘手的一件事是因为这个b是五，这个b也必须是五个这对C没有整数是有效的，五次没有什么可以给你33，至少没有给出c是一个整数。所以有时你必须备份并再次尝试，所以这三个和五个组合必须是错误的，所以让我们重新开始。而不是三次五，让我们尝试五次将解决我们的问题。我们仍然有五次三倍为十五，所以很好，但现在B是三，我们将能够使这个陈述是真的。33次是33次？三次11.所以我们击败了这个问题的所有限制，我们已经准备好解决了这个问题。 The question is which of the following must be true? So actually we kind of have to look at the answer choices in order to solve the problem and that's where we get to our new guideline which is that sometimes variables have to be turned into numbers. For instance to know whether B is greater than A is greater than C is true, got to put the numbers in. So let's do that what was B? B was three, so three is greater than A, that was five is greater than C which was 11, not so much three is not greater than either of those, so we'll get rid of that one. B; A is greater than C is greater than B, A is five is greater than C which is 11, we can actually quit here 'cause five is not greater than 11. C; C is greater than A that's 11 which is greater than A which is five and is that greater than B which is three? Yes. We've found our answer so we can quit now. So the principle here is that sometimes you have to take your answer choices and also make them numerical, if they're not already numerical. Let's look at one more example of that idea.

'如果q = rs以下哪个必须等于qs？'所以再次我们需要选择一些数字，这是一个小小的技巧，如果我们选择Q，那么找到易于处理的r和s很难解决，所以我们应该先选择r和s，然后才能确定什么q必须是什么。也一般来说，我们希望避免第一个和两个，所以让我们尝试三个，然后四次尝试三次，然后三次让Q 12。所以我们已经选择了数字，我们已经准备好了第二步，我们已经准备好了第二步，回答这个问题。问题基本上是QS等于的问题，所以让我们这样做。q是12，s是四个，所以qs等于什么？48所以这是我们的答案，我们准备在选择中寻找一个比赛，但等待它们的变量不是数字，所以我们需要将它们转化为数字，然后我们可以找到匹配。所以让我们做所有的插头。r平方时间s是三个平方时间，这是九次四个是36的，这不是48的匹配.b; b;Q squared over R Q squared is 12 squared that's 144 divided by R which is three and that does turn out to be 48. Now it's up to you at this point whether you think that you want to quit because you usually will not find more than one match but just to be safe you should generally keep on going. So we tentatively think that this is our answer but to be safe, let's do the rest. C is R over Q that's three twelfths that's a very small fraction nowhere close to 48, so we're done. D is R squared over S that's three squared over four that's also a relatively small fraction, nowhere near forty eight it's out and S squared over R that is four squared which is 16 over R which is three, still a relatively small number definitely not 48. And so we've confirmed that the right answer is indeed B.
所以有那种策略，但让我们看看另一个右手？这就是有时候你会发现不止一个正确的答案，并在发生这种情况时记住你回去改变你的答案，你继续这样做，直到你把它缩小到一个答案的一个答案选择，无论如何你选择的是什么数字。所以让我们试试这个;'如果零小于x小于1，则-1小于y小于零，以下哪个必须是真的？所以让我们开始选择一个值，让我们尝试x等于四分之一，y等于负面，让我们看一半。好吧，x平方是否大于y平方？好吧，这将是一个十六分之一，这一个是第一个，第十六个较小，所以这对我来说很好。现在x减去y大于零什么？四分之一减去一半是四分之一加一半，最终是四分之三，是四分之三大于零？ Yes it is so we're going to have to leave B in, it might be the right answer or it might just work with these particular numbers. Let's try C; Y minus X is greater than zero so that would be negative one half minus a quarter that's negative three quarters that's not greater than zero, so we eliminate that one. D, x+y is greater than zero, that's one quarter plus negative one half that's negative a quarter not greater than zero, so that's out. Looks like we're doing pretty good let's see how E treats us x+y is less than zero, well we just did that one right? And it was negative a quarter, so negative a quarter is less than zero also true, so we actually have it narrowed down to two choices.
所以我们实际上并不知道正确的答案是什么，但我们可以选择x和y的新价值，再次看到任何两个答案的选择不可能继续工作。所以让我们将其混合在X的大小小于Y的大小，技术上我应该使用字幅度。所以让我们混合起来，让我们尝试将x成一半，仍然是积极的“因为它必须是和制作y负一季度仍然是一个消极的”原因它必须然后让我们看看这次影响如何x-y is one half minus negative a quarter that ends up being three quarters and it's greater than zero sounds good, still true. Down here let's see if this looks true x+y is less than zero, one half plus negative a quarter well that's one quarter less than zero? No longer true, so we've managed to eliminate E, B remains true so we've found our answer. There's more than one correct answer at first but by changing numbers we were able to narrow it down to just one right answer.
我们再看一个例子，如果-1小于n小于1 n不等于0下面哪个选项是正确的?我们选一个数试试N = 1 / 2。我们必须确保在- 1和1之间，很多人很自然地选择整数，所以我们会尝试1或2或3但这显然违反了规则，所以要小心。现在我们来看看什么是对的- 1 / 2小于1 / 2是对的吗?对，这样就可以把A留在里面了。1 / 2是否小于1 / 2的平方也就是1 / 4 ?不，1 / 2实际上更大，所以B出来了。它们是否刚好相反1 / 4是否小于1 / 2 ?这是对的，所以我们把C留作选项。N的立方等于1 / 8,1 / 8小于N的平方这是1 / 2的平方，也就是1 / 4,1 / 8小于1 / 4，我们把这个留在这里。 And E is it true that one half is less than one half cubed which is one eighth, nope that's out too.
你们可以看到我们还有很多工作要做。我们把它混合一下，这次既然我们尝试了正分数我们尝试了负分数我们想要一个不同的数。但为了简单起见，我们可以用- 1 / 2因为我们知道如何有效地处理1 / 2。看A - N现在等于1 / 2它小于N - 1 / 2吗?现在没有A，我想指出我们经常认为负号意味着我们处理的是一个负数，但这不是真的。在A中，N的值是- N意味着符号的改变不再意味着它是一个负数而是意味着它变成了一个意想不到的正数。C;N的平方是- 1 / 2的平方，这是1 / 4小于N的平方是- 1 / 2吗?不，负数并不大，实际上它更小，所以C出来了。看起来D是正确答案但是我们来验证一下N³是- 1 / 8因为要记住负数