I've never seen the arch symbol before... What does it mean? The book explains the answer, but the answer is no help when I don't understand the context of the problem.
Had to do quite a bit of research to find this answer, and finally located it on wikipedia! (Funny how it's always the last place you look, eh?)
A ∪ B means the set of those elements which are either in A, or in B, or in both
A ∩ B means the set that contains all those elements that A and B have in common
Those symbols do show up in a few SAT prep books. I would expect that the authors of such books are aware of exactly what is covered and what is not on the SAT (but of course, this might not be the case).
I would expect that the authors of [...] books are aware...
This is a common misconception that illustrates the power of the printed word: if it's printed it's gotta be true. Be aware: that which you see in print ain't necessarily so.
(but of course, this might not be the case)
- a nice disclaimer clause!
It has been pointed out so many times on the CC that in your SAT practice you should stick with the CB authentic resources (there are plenty of them for the SAT I; SAT Subject tests is a different matter).
SAT questions from other than the CB sources are often ambiguous, outside of the SAT scope, overly difficult, and so on - which means, among other things, that creators of those questions are either not aware of exactly what is covered and what is not on the SAT or don't give a hoot about it.
^ Amen to all that. And let me add one other reason to practice with CB material only: timing! Timing is a HUGE factor on the SAT. You simply cannot get real feedback about how you are doing in that department when you work with fake tests.
knowthestuffPosts: 109Registered UserJunior Member
^
No. E (3/14)
Method 1 (works if you don't know that much about probability)
A = {1, 2, 4, 8}
B = {1, 3, 6, 8, 9}
C = A U B = {1, 2, 3, 4, 6, 8, 9}
D = A intersection B = {1, 8}
So here are the possible combinations, where the first number c is from C and the second number d is from D
1&1, 1&8, 2&1, 2&8, 3&1, 3&8, 4&1, 4&8, 6&1, 6&8, 8&1, 8&8, 9&1, 9&8 (14 combinations)
Of the above combinations, only 1&1, 3&1, and 9&1 yield an odd product. (3 combinations)
So the probability of choosing c and d so that cd is odd is 3/14.
Method 2 (how I prefer to solve the problem)
For the product of two integers to be odd, both numbers must be odd.
The probability of picking an odd number for C is 3/7
The probability of picking an odd number for D is 1/2
The probability of picking an odd number for C as well as for D is 3/7 * 1/2 = 3/14
Replies to: Math Q
A ∪ B means the set of those elements which are either in A, or in B, or in both
A ∩ B means the set that contains all those elements that A and B have in common
List of mathematical symbols - Wikipedia, the free encyclopedia
I think you should have learned some basics in middle school.
@Archite -
You'll never see these symbols on the SAT.
So the question is - as reiterated on CC gazillion times - why bother with the non-CB questions?
It has been pointed out so many times on the CC that in your SAT practice you should stick with the CB authentic resources (there are plenty of them for the SAT I; SAT Subject tests is a different matter).
SAT questions from other than the CB sources are often ambiguous, outside of the SAT scope, overly difficult, and so on - which means, among other things, that creators of those questions are either not aware of exactly what is covered and what is not on the SAT or don't give a hoot about it.
No. E (3/14)
Method 1 (works if you don't know that much about probability)
A = {1, 2, 4, 8}
B = {1, 3, 6, 8, 9}
C = A U B = {1, 2, 3, 4, 6, 8, 9}
D = A intersection B = {1, 8}
So here are the possible combinations, where the first number c is from C and the second number d is from D
1&1, 1&8, 2&1, 2&8, 3&1, 3&8, 4&1, 4&8, 6&1, 6&8, 8&1, 8&8, 9&1, 9&8 (14 combinations)
Of the above combinations, only 1&1, 3&1, and 9&1 yield an odd product. (3 combinations)
So the probability of choosing c and d so that cd is odd is 3/14.
Method 2 (how I prefer to solve the problem)
For the product of two integers to be odd, both numbers must be odd.
The probability of picking an odd number for C is 3/7
The probability of picking an odd number for D is 1/2
The probability of picking an odd number for C as well as for D is 3/7 * 1/2 = 3/14