1. If -13 < a < -2 and 1 < b < 9. Which of the following could be equal to the product of ‘a’ and ‘b’. Indicate all possible values.
-20
-18
-15
-14
-13
-9
Your
answer of -20 -18 -15 -14 -13 -9 was incorrect.
Correct
answer is: -15 -14
Explanation:
This can be
solved by simply multiplying the respective numbers i.e.
(-13)(1)
< ab < (-2)(9) -> -18 < ab < -13
*답은 ab의 범위인 -12*8=-72 부터 -1*0=-0까지 아닌가요?
2. If a and b are two of the solutions of the equation x^3-x^2-6x= 0, with a≠ 0 and a ≠ b, then which of the following could be the graph of x/a > b ? Indicate all such graphs.
The
correct answers are A, B, and D.
Begin by
scanning the answer choices in order to see what type of answers to look for.
Next, work out the math in the question, and see which answer choices fit your
results. First, manipulate the equation x^3-x^2-6x= 0. Factor out an x
from each term: x(x^2-x-6 ) = 0
Then factor the quadratic expression, using reverse FOIL (First, Outside, Inside, Last). Remember that x^2-x-6 = (x+a)(x+b), where ab = −6 and a b + =−1 , the coefficient of x. The numbers 2 and –3 for a and b are the only ones that qualify, so the expression becomes x(x+2)(x-3)= 0 .
Thus, the possible solutions of the equation are x = 0, x = –2, and x = 3. All three of these solutions are possible values for b and the possible values for a are –2 or 3. There are four different possibilities:
1. If a = −2
and b = 0 , then x < 0 (Remember that
multiplying both sides of an inequality by a negative number reverses the
direction of the inequality.) The graph of this inequality appears in answer
choice A.
2. If a = −2
and b = 3 , then x < −6 . The graph of this inequality appears in choice B.
3. If a = 3
and b = 0 , then x > 0 . The graph of this
inequality is not listed.
4. If a = 3
and b = −2 , then x > −6 . The graph of this inequality appears in choice D.
* 왜 A인지 해설이 이해가 안됩니다. x값은 -2와 3으로 나왔는데 해설중 빨간색으로 해놓은 부분, 왜 b에 0을 대입하나요?
3. ABCD
is a rectangle. E is the intersection of AD and BC.
A. Quantity
A is greater.
B. Quantity
B is greater.
C. The two
quantities are equal.
D. The relationship cannot be determined from the information given.
The
correct answer is C.
Any values
that are assigned to the side lengths of the figure will result in the two
areas being equal. This is true for both whole and fractional values.
4. 3번문제와 연결된 문제 입니다.
Quantity A Quantity B
(AB)^2+(BD)^2 AD
A. Quantity
A is greater.
B. Quantity
B is greater.
C. The two quantities
are equal.
D. The
relationship cannot be determined from the information given.
The correct answer is D.
If whole
number values are assigned to the side lengths of this right triangle, then
answer choice A would be correct. If fractional or decimal values (less than 1)
are assigned to the side lengths of this right triangle, then answer choice B
would be correct. Therefore, the correct answer is D.
*AB^2+BD^2 = AD^2이니까 그냥 AD이면 Quantity A보다는 작은거 아닌가요?
5. A
regular, six-sided die is rolled three times. What is the probability that each of the three rolls will produce an odd number?
The
correct answer is 1/8.
Three of the
die’s six sides feature odd numbers, so the probability that any given roll
will produce an odd number is 3/6 or 1/2. Each roll of the die is independent of the
others, so the probability that each of the three rolls will produce an odd
number is (1/2)^3 or 1/8.
*저는 처음에 답을 D(1/8)로 했다가 A(1/2)로 바꿨어요. 왜냐면 3번을 연속으로 던졌을때의 확률은 1/8인데 the probability that each of the three rolls 중, each라는 단어 때문에 한번 던질경우의 수니까 ½로 선택했어요.
6. If p
and q are integers, and n is an odd integer that is a factor of both 2p and q,
then n is a factor of which of the following?
The correct
answers are A, B, C, and D.
*저는 C가 이해가 안됩니다.
7. The local baseball team employs at least 3 times as many pitchers as catchers, but never more than 11 players total. Pitchers make an average of $45,000, and catchers make an average of $30,000. Which of the following amounts are the possible averages for all the pitchers and catchers, rounded to the nearest dollar?
The
correct answer is D.
The
only combination of pitchers and catchers that apply are 3 pitchers/1 catcher and
6 pitchers/2 catchers. Both
combinations leave you with the same answer: 41,250.
*저의 답은 D, E, F, G, H 인데,
해설중 빨간부분이 이해가 안됩니다. 왜 꼭 3:1비율이어야 하죠?
최대 11명까지 뽑으니까 9:2 혹은 10:1도 가능한거 아닌가요?
8. The
projections for the coming year indicate an increase of 10 percent in the
average cost of gas. How much more per day will the company pay out on average
for gas for the first 6 months of next year?
A. $9
B. $12
C. $15
D. $18
E. $21
The correct answer is A.
16 + 10 + 29 + 9 + 16 + 14 = 94. 94 × 1.10 = 103. 103 – 94 = 9
*해설중 103에서 평균을 구해야 하는까 6으로 나눠줘야 하는거 아닌가요? 103/6 = 17.1666이고 94/6 = 15.6666. 그래서 차를 구하면 17.16666 - 15.77777 = 1.5.
9. W<X<Y<Z
Quantity A Quantity B
W+Y X+Z
The
correct answer is B.
*저는 D를 선택했어요.
*
10. It
takes 3 electricians four 8-hour days to wire a house. If the general
contractor wanted the house wired in three 8-hour days, how many electricians
should he have hired?
The
correct answer is 4.
Set up an
equation: (32)(3) = 24x. 4 = x
* 3:32hrs = x:24hrs로 풀었어요. 그럼 32x = 72, 따라서 x=2.25여서 3명을 선택했는데 답은 4명으로 나와있어요.
상식적으로 4일하는데 3명이 필요한데 같은시간을 3일 일하면 같은 명수의 사람이나 더 적은 인원이 필요한거 아닌가요? 이해가 되지않아 헷갈립니다.