 |
Опрос |
 |
|
Пример задания Problem Solving с подробными комментариями: ''Probable P's and Q's''
Probable P's and Q's
Question
If p2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 3/10
Answer
If we factor the right side of the equation, we can come up with a more meaningful relationship between p and q: p2 – 13p + 40 = q so (p – 8)(p – 5) = q. We know that p is an integer between 1 and 10, inclusive, so there are ten possible values for p. We see from the factored equation that the sign of q will depend on the value of p. One way to solve this problem would be to check each possible value of p to see whether it yields a positive or negative q.
However, we can also use some logic here. For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
|
|
|
|
|
|
|
Guard Patrol
The organizers of a week-long fair have hired exactly five security guards to
patrol the fairgrounds at night for the duration of the event. Exactly two
guards are assigned to patrol the grounds every night, with no guard assigned
consecutive nights. If the fair begins on a Monday, how many different pairs of
guards will be available to patrol the fairgrounds on the following Saturday
night?
A) 9
B) 7
C) 5
D) 3
E) 2
|
|
Вверх 
