<p>Hi, could you please help me with this math question from dr.chung's sat math?
the question said: a and b are different positive integers and a is greater than b.
if a^2-b^2 = 7, what is the value of ab?
a) 6
b) 8
c) 10
d) 12
e) 14</p>
<p>the solution said a^2-b^2 = (a+b)(a-b)=7 i understand this part but then it said
a+b =7 and a-b = 1... I don't understand this part. When it equals to 7, does a+b automatically became 7? Thank you in advance!</p>
<p>Break up a^2 - b^2 into two integer factors. You get (a-b) and (a+b). Since a and b are both positive integers (a-b) and (a+b) must also be integers using common sense. If multiplied together they make 7, and 7 is prime, one factor must equal 1 and the other factor must equal 7. Using common sense and the fact that a and b are both positive we deduce that a-b < a+b, therefore we have a-b = 1 and a+b = 7. Using middle school algebra we solve these two equations to get a = 4 and b = 3. Therefore ab = 12 and your answer is D.</p>
<p>Here’s another approach: don’t go right into algebra mode – look at the equation and think about what it means: a^2-b^2=7 means that when you take the difference between two squares, it comes out to 7. And you know they are integers…and 7 is pretty small. It’s a good bet that the integers you seek are pretty small too. Takes about 10 seconds of playing to find that 4^2 - 3^2 = 16 - 9 =7. So 4 and 3 are your integers…product is 12.</p>
<p>CAREFUL!!! This is something you will never encounter on the SAT. Do only questions from actual tests and take others JUST as concepts books, or even not at all. I’m sorry for being rough but I’m afraid you might pick up habits or concepts you won’t need and that is just wasting time, but not only that; it is detrimental to your score. Math on the SAT uses basic concepts a 7th grader should know. What makes the section tricky is when the College Board uses the concepts in a way in which you won’t normally see them. For example, this question requires algebra 2. That is not on the SAT. How do you realize this? Look at it this way. You are the College Board and need to make an international exam that is standardized (same and fair for everyone) as well as acceptable to colleges. How do you do that for math? Should you test advanced concepts? No, because that’s what AP exams are for as well as normal school grades. Should you test basic concepts? No, because then everyone would get perfect. So what do you do? You test basic concepts in strange ways, not normally encountered in schools, so that you have to use logic. You can’t test advanced concepts in strange ways because not everybody takes advanced courses, which would cause an issue for the College Board. Stick to real questions. Study ONLY what’s going to come so that you don’t go outside and pick up bad habits. I suggest the SAT Prep Black Book, since it uses logic and puts you through the sections of the Blue Book practice tests to show you really how to answer.</p>
<p>Interestingly enough, the problem might be one of those rare Chung’s problems that is not irrelevant. And one of the rare solutions that is remotelty intelligible. </p>
<p>The a^2-b^2 = (a+b)(a-b) is a formula that is part of the SAT, and one that is useful to remember. And so are the first prime numbers. All in all, it is not a bad SAT question.</p>
<p>However, however, this does not change anything about the value of Chung’s book. It is still pure junk. Thus, OP do yourself a huge favor and toss that garbage book in the bin. With the availability of useful resources why waste your time trying to decipher the quasi English used in a most irrelevant book?</p>
<p>thank you guys so much! is Dr. Chung that bad?</p>
<p>This question is somewhat relevant to the SAT as far as the difference of squares equation is concerned and solving the resulting equations. I have attached an image of an official SAT question that in my opinion would come closest to this concept. </p>
<p>[Official</a> SAT Question - Dabral’s library](<a href=“http://www.screencast.com/t/2dKa5YoHUq]Official”>http://www.screencast.com/t/2dKa5YoHUq)</p>
<p>However, I still have not seen a question on the official SAT that goes along the line of: Given pq=13, where p and q are integers and p>q, what is the value of p+q? In this case because 13 can only be expressed as a product of two integers in only one way, we can solve such an equation. But I have yet to see such a question on the SAT. I won’t be surprised if they do test this concept, because it is tested on the GRE and GMAT, also written by ETS, the writers of SAT.</p>