Answer: A
Solution:
We can express the number of inches of rain in a ratio, 366inches/1month =366 inches/(31*24)hours .
Answer: A
Solution:
For positive numbers, the larger the number, the smaller its reciprocal. Likewise, smaller numbers have larger reciprocals. Thus, all we have to do is find the smallest number. 1/3 is the smallest number.
Answer: C
Solution:
To find the smallest sum, we just have to find the smallest 3 numbers and add them together.
Obviously, the numbers are-3, -1, 7, and adding them gets us 3.
Answer: C
Solution:
40.3+0.07=40.37=40， 40*1.8=72. 72 is the closest to 72, so the answer is C.
Answer: D
Solution:
There are 60 minutes in an hour. 1000 minutes=16 hours+40 minutes. So, the contest end at 4: 40 am.
Answer: E
Solution:
=2/(1/3)=2*3=6.
Answer: B
Solution:
Let the number is x. x>sqrt(8) => x>2; X<sqrt(80) => x<9;
So ,there are : 3,4,5,6,7,8, totally 6 numbers.
Answer: E
Solution:
2*B has a units digit of 6, so B is either 3 or 8. If B=3, then the product is 32*73, which is clearly too small, so B=8.
Answer: E
Solution:
There is 1 way to get from C to N. There is only one way to get from D to N, which is DCN.
Since A can only go to C or D, which each only have 1 way to get to N each, there are 2 ways to get from A to N.
Since B can only go to A, C or N, and A only has 2 ways to get to N; C only has 1 way and to get from B to N is only 1 way, there are 2+1+1=4 ways to get from B to N.
M can only go to either B or A, A has 2 ways and B has 4 ways, so M has 4+2=6 ways to get to N.
Answer: B
Solution:
Let's say that the distance from the picture to the wall is x. Since that distance will be on both sides of the picture (it's in the exact middle), we can say that
x+3+x=19, so x=8.
Answer: A
Solution:
3*5 *8 means （(3+5)/2） * 8=4 * 8=（4+8）/2=6.
Answer: D
Solution:
We need to find the number of those who did get the same on both tests over 30 (the number of students in the class). So, we have (2+4+5+1+1)/30 =40%.
Answer: C
Solution:
The perimeter of the requested region is the same as the perimeter of the rectangle which length is 8 and width is 6. This makes the answer 2*(6+8)=28.
Answer: C
Solution:
b/a will be largest if b is the largest it can be, and a is the smallest it can be.
Since b can be no larger than 1200, b=1200. Since a can be no less than 200, a=200.so b/a=1200/200=6.
Answer: B
Solution:
180*50%*20%=72.
Answer: A
Solution:
What we want to find is the number of hamburgers sold in the winter. Since we don't know what it is, let's call it x. From the graph, we know that in Spring, 4.5 million hamburgers were sold, in the Summer was 5 million and in the Fall was 4 million. We know that the number of hamburgers sold in Fall is exactly 1/4 of the total number of hamburgers sold, so we can say that: 4/(4.5+5+4+x)=1/4. So x=2.5.
Answer: E
Solution:
Let's say that n is odd. If n is odd, then obviously n*o will be odd as well, since o is odd, and the product of two odd numbers is odd. Since o is odd, o*o will also be odd. And adding two odd numbers makes an even number, so if n is odd, the entire expression is even.
Let's say that n is even. If n is even, then n*o will be even as well, because the product of an odd and an even is even. O*O will still be odd. That means that the entire expression will be odd, since the sum of an odd and an even is odd.
Looking at the multiple choices, we see that our second case fits choice E exactly.
Answer: B
Solution:
The shortest possible rectangle that has sides 36 and 60 would be if the side opposite the wall was 60.
Each of the sides of length 36 contribute 36/12+1=4 fence posts and the side of length 60 contributes 60/12+1=6 fence posts, so there are 4+4+6=14 fence posts. However, the two corners where a 36 foot fence meets an 60 foot fence are counted twice, so there are actually 14-2=12 fence posts.
Answer: D
Solution:
The first six gallons are irrelevant. We start with the odometer at 56,200 miles, and a full gas tank. The total gas consumed by the car during the trip is equal to the total gas the driver had to buy to make the tank full again, i.e., 12+20=32 gallons. The distance covered is 57060-56200=860 miles. Hence the average MPG ratio is 860/32=26.9.
Answer: D
Solution:
=300^5/(30*400^4)=(3^5*10^10) / (3*4^4)*10^9=3^5*10/(3*4^4)
=3^4*10/(4^4) =810/256 which is closest to 3.
Answer: E
Solution:
The four squares we already have assemble nicely into four sides of the cube. Let the central one be the bottom, and fold the other three upwards to get the front, right, and back side. Currently, our box is missing its left side and its top side. We have to count the possibilities that would fold to one of these two places.
A would be the top side - OK
B would be the left side - OK
C would cause the figure to not be foldable at all
D would be the left side - OK
E would be the top side - OK
F is the same case as B - OK
G is the same case as C
H is the same case as A - OK
In total, there are 6 good possibilities.
Answer: C
Solution:
Let's say that Alan gets an A. Well, from his statement, then Beth would also get an A. But from her statement, Carlos would get an A. And from his statement, Diana would also get an A. So all 4 would get A's, but the problem said only 2 got A's.
Let's say that Beth gets an A. From her statement, we know that Carlos get an A, and from his statement we know that Diana gets an A. But that makes 3, which is not 2.
If Carlos gets an A, then Diana gets an A. That makes 2, so C is the right answer.
Answer: B
Solution:
The small circle has radius 1, thus its area is Pi.
The large circle has radius 2, thus its area is 4*Pi.
The area of the semicircle above AC is then 2*Pi.
The part that is not shaded are two small semicircles. Together, these form one small circle, hence their total area is Pi. This means that the area of the shaded part is 2*Pi-Pi=Pi. This is equal to the area of a small circle, hence the correct answer is 1.
Answer: B
Solution:
The probability of A1 in group 1 is 1/3; The probability of Bod in group 1 is 1/3; The probability of Carol in group 1 is 1/3; So , The probability of A1, Bob, Carol all in group 1 is 1/3 * 1/3 * 1/3=1/27. The probability of A1, Bob, Carol all in group 2 or group 3 is 1/27 too. Thus the probability that A1, Bob ,Carol will be assigned to the same lunch group is 1/27+1/27+1/27=1/9.
Answer: D
Solution:
From 1 to 101 there are 50 multiples of 2, and their average is (2+100)/2=51. Similarly, we can find that the average of the multiples of 3 between 1 and 101 is (3+99)/2=51. the average of the multiples of 4 is (4+100)/2=52. the average of the multiples of 5 is (5+100)/2=52.5. and the average of the multiples of 6 is (6+96)/2=102, so the one with the largest average is D.
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