<p>So instead of going through the trouble of figuring out the combined time we are saying it’s T and then comparing rates??</p>
<p>Yes, the exact time doesn’t matter. If you were to look at the work halfway done, for example, the fraction each person did would be the same as if they finished. If you wanted to find T, you could set my denominator of T/3+T/4+T/6 equal to 1, but this isn’t necessary.</p>
<p>Ok, this question is from Barron’s. </p>
<p>If the difference of two numbers is less than the sum of the numbers, which of the following MUST be true?</p>
<p>A) neither is positive
B) at least one of the numbers is positive
C) exactly one number is positive
D) both numbers are positive
E) none of these statements must be true</p>
<p>Let the two numbers be a and b, where a<=b. Then b-a<a+b or="" a="">0 so 0<a<=b. Both are positive. D. </a+b></p>
<p>I find this question to be slightly ambiguous. I interpreted “the” difference of a and b to mean the larger of a-b and b-a, but I suppose it could also mean a-b, in which case only one number need be positive (B). I didn’t chose this interpretation because it would mean that the difference of a and b isn’t the same as the difference of b and a. In any event, I don’t like the wording. The issue is basically if you consider the difference of 2 and 5 to be 3 or -3.</p>
<p>This is a bad question. “The difference of two numbers” has no meaning. Sometimes in basic algebra I’ve seen “the difference between a and b” interpreted as b - a, but I think this is poor wording as well. If the College Board were to include a question with more than one interpretation on the SAT it would create a huge media stir, and the question would be excluded from scoring.</p>
<p>Ok, I’m glad that I’m not the only person who found this question ambiguous. @tau628 what did Barron’s say was the answer? I imagine either B or D, but it does depend on interpretation it seems.</p>
<p>I put D, but Barron’s says it’s B 
</p>
<p>Ok, then the logic is that if a and b are the numbers, then the difference is interpreted as a-b without regard to which one is larger. So a-b<a+b is="" solved="" exactly="" when="" b="">0 and there is no constraint on a. It just depends on what the difference of two numbers is interpreted to mean.</a+b></p>
<p>^I respect your math ability very much, but don’t you think it would be better to suggest that people ignore the non-CB questions? It just doesn’t seem to me to be an efficient way of studying.</p>
<p>I don’t know, some other sources have good questions. I’ve had good experiences with other sources when I was studying for SAT/SAT IIs/APs. There is the occasional bad question/typo, but for learning purposes they can be quite good.</p>
<p>I’m just trying to build skills really w/ Barron’s since it’s summer. I’m gonna start Blue Book soon. </p>
<p>Anyway, I had another Barron’s question
25 students took a quiz, and the grades they earned ranged from 2 to 10. If exactly 22 of them passed by earning a grade of 7 or higher, what is the highest possible average the class could have earned on the quiz. </p>
<p>I just don’t get book explanation</p>
<p>If this ends up being a bad question too, I’m going to have to insist that you give up the book and find a better one :)</p>
<p>Another poorly worded question, as it is unclear if the quiz grades need to be integers. I suppose they have to be - otherwise there would not be a maximum. But the question absolutely needs to specify this. </p>
<p>I agree with DrSteve. I suppose the answer in the book is that the maximum occurs when everyone who passed got the highest possible score of 10/10 and the three people who failed got the highest failing score of 6/10 (there would be no highest failing score if the scores didn’t have to integers as @DrSteve correctly pointed out) except for the person who got a 2/10. Then the average is (10<em>22+6</em>2+2)/25=9.36. </p>
<p>How do you know one of the guys is going to get a 2/10 for sure? </p>
<p>Also, how do I know which questions are “bad” from this book?</p>
<p>While i typically do well in high school math classes, standardized test math seems to elude me which is why I’m using as many resources as I can possibly find. </p>
<p>It says the grades ranged from 2 to 10, so I interpreted this as saying that the lowest grade was a 2 and the highest was a 10. It does seem like it’s not the most precise book; maybe try the blue book or some other resource.</p>
<p>Even this is not clear. “The grades range from 2 to 10” can have two possible meanings - the actual grades or the possible grades - bad, bad question.</p>
<p>Yeah, that’s a question of poor quality. I would assume that someone scored 2, but one shouldn’t readily make that assumption. Also, if the scores are not integers, then the best case scenario is 22 students get 10, one student gets 2 and the other two students get 6.9 or 6.99999 or whatever.</p>
<p>I’ve been writing math problems for mock exams (not SAT) so it is not hard to spot ambiguous or otherwise poorly-written SAT questions. Maybe I should write my own SAT math book :)</p>
<p>Question From S.AT. Blue Book {College Board} Page 17
In the figure above, PQ is a straight line. Which of the following must be true about x and y?
[A] x + y = 180
** 90 + x = 180-y
[C] 90 + x= y
[D] 2x= y
[E] 2y=x
I eliminated C/E/D
The answer is B
My question is why can’t it be A or C
How can you find out what is x and y?</p>
<p>@HopeToPast Because PQ is a straight line, all the angles on one side of it must equal 180. The three angles on one side of PQ are x, y, and a right (90 degree) angle. Thus, x+y+90=180. That can be rearranged to be x+90=180-y, which is b.</p>