Answer: D
Solution:
C and D are the only answer choices where the numerator is close to half of the denominator. 3/8 =0.375 and 5/12=0.41. Thus the answer is 5/12.
Answer: D
Solution:
=(1+2+3+…+9)/10 +55/10 =45/10 + 55/10=100/10 =10.
Answer: C
Solution:
8 hours from 7:25 AM is 15:25 or 3:25 PM. 45 minutes from 25 minutes is 10 minutes after the hour, so her working day ends at 4:10 PM.
Answer: B
Solution:
Rotating the circle 120° is 1/3 of a full turn. Going 1/3 clockwise of a full loop around the circle, the triangle would replace the square, the square would replace, the circle, and the circle would replace the triangle, B.
Answer: B
Solution:
1 mile=8 furlongs=8*40 rods=320 rods.
Answer: A
Solution:
Method 1: Within six consecutive integers, there must be a number with a factor of 5 and an even integer with a factor of 2. Multiplied together, these would produce a number that is a multiple of 10 and has a units digit of 0.
Method 2: We can easily compute the product of the first 6 positive integers: 1*2*3*4*5*6. Therefore the units digit is 0.
Answer: B
Solution:
The sum of the angles in a triangle is 180°. We can find <ABE=180-60-40=80, so <CBD=180-80=100. <BDC=180-100-30=50.
Answer: C
Solution:
Because 8+8+8=24, it follows that one of the digits must be a 9. The other two digits them have a sum of 25-9=16. The groups of digits that produce a sum of 25 are 799 or 889 and can be arranged as follows 799, 979, 997, 889, 898, 988. The number of configurations is 6.
Answer: A
Solution:
After the 20% sale, the coat costs 100*0.8=80 dollars. Then 5 dollars are taken off for a cost of 80-5=75. Adding on the sales tax, the final amount is 75*1.08=81.
Answer: A
Solution:
We should list all the positive divisors of 36 and count them. By trial and error, the divisors of 36 are found to be 1,2,3,4,5,6,12,18,26, for a total of 9 (Method 2: 36=4*9=2^2 * 3^2; so 36 have (2+1) * (2+1) =9 factors.) . However, 1 and 2 can't be expressed as N+2 for a POSITIVE integer N, so the number of possibilities is 7.
Answer: B
Solution:
40 students and 20 of the girls were from Jonas Middle school , so there are 20 boys were from Jonas Middle School. There are total 52 boys ,so 52-20=32 boys were from Clay middle school.
Answer: A
Solution:
Square II clearly has 1/4 shaded. Partitioning square I into eight right triangles also shows 1/4 of it is shaded. Lastly, square III can be partitioned into sixteen triangles, and because four are shaded, 1/4 of the total square is shaded.
Answer: C
Solution:
The number halfway between is the average. (1/4+1/6)/2=5/24.
Answer: E
Solution:
There are 2*90=180 minutes of total playing time. Divided equally among the five children, each child gets 180/5=36 minutes.
Answer: A
Solution:
Notice the pattern from 0 to 4 repeats for every four arrows. Any number that has a remainder of 0 when divided by 4 corresponds to 0.
The remainder when 425 is divided by 4 is 1. The arrows from point 425 to point 427 correspond to points 1 and 3, which have the same pattern as A.
Answer: E
Solution:
Let a be the side length of one square, and b be the side length of the other, where a>b. If the perimeter of one is 3 times the other's, then a=3b. The area of the larger square over the area of the smaller square is : (a*a)/(b*b)=(3b *3b)/(b*b)= (9*b*b)/(b*b)=9.
Answer: D
Solution:
Her driveway has 4*10*3=120 cubic yards of snow. After the first hour she would have 120-20=100 cubic yards, then 100-19=81,81-18=63, 63-17=46,46-16=30,30-15=15,15-14=1 cubic yard after the seventh hour. It will take her a little more than seven hours to shovel it clean, which is closest to 7.
Answer: B
Solution:
When Mike is shopping at the mall, his distance doesn't change, so there should be a flat plateau shape on the graph. This rules out C,D,E. The portion of graph in which the distance is changing is linear, inconsistent with how he changes speed from the city and the highway. The best representation of his travels is graph B.
Answer: E
Solution:
The radius of each semicircle is 2, half the side length of the square. The line straight down the middle of square ABCD is the sum of two radii and the length of the smaller square, which is equivalent to its side length. The area of ABCD is (2+4+2)*(2+4+2)=64.
Answer: D
Solution:
to make the smallest fraction, you need the lowest numerator and the highest denominator. So, take the first 2 and last 2 digits of the set: 1,2 and 8,9. Balance the equations to be "even". Since 1 is smaller than 2, put it over 8. You get 1/8 + 2/9 = 25/72.
Answer: C
Solution:
If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.
Answer: D
Solution:
An even sum occurs when an even is added to an even or an odd is added to an odd. Looking at the areas of the regions, the chance of getting an even in the first wheel is 1/4 and the chance of getting an odd is 3/4. On the second wheel, the chance of getting an even is 2/3 and an odd is 1/3.
1/4 *2/3 + 3/4 * 1/3=5/12.
Answer: C
Solution:
To maximize the hundreds digit, Let X=9, then, the sum is a 4-digit number. So ,we let x=8 and y=9, Thus: 888+98+8=994, which has the form YYZ.
Answer: B
Solution:
Case 1: There are no green squares.
Case 2: one green square and three red squares. This can only be done when the green square's top and right edges are against the edge. 1 .
Case 3: two green squares and two red squares. This happens when the two green squares are in the two top squares or two right squares, 2 .
Case 4: three green squares and one red square when the red square's left and bottom edges are against the edge. 1 .
Case 5: four green squares and zero red squares.
1+1+2+1+1=6.
Answer: A
Solution:
Notice that: 9*4=36 and 3+6=9=9*1;
99*44=4356 and 4+3+5+6=18=9*2;
999*444=443556 and 4+4+3+5+5+6=17=9*3.
Therefore the answer is 9*94=846.
中文解析：
我们不可能真的计算94个9乘以94个4的乘积，尝试去找规律:
一个9乘以一个4是36, 每位数字的和是3+6=9；
两个9乘以两个4是4356， 每位数字的和是： 18;
三个9乘以三个4是443556, 每位数字的和是： 27；
发现其规律: 9*1； 9*2； 9*3；
则94个9乘以94个4的结果， 每位数字的和是： 9*94=846. 答案是A。
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