Term
GRID IN:
On a number line point D has a coordinate of 8 and point F has a coordinate of 12. What is the coordinate of point E which is midway between D and F?


Definition
The distance between the points on the number line is 20 units. Midway would be ten units from either end= 8+10=2 


Term
GRID IN:
120 percent of what number is equal to 45 percent of 80? 

Definition
120/100x n.
n= 90/100x160
n= 90x160/120=120 


Term
MULTIPLE CHOICE:
If the product of 12 integers is negative, at most how many of the integers can be negative? 

Definition
A. 7
B. 8
C. 9
D. 10
E. 11
Multiplying four negatives (or any even multiple) results in a positive. But multiplying six negatives (or any odd multiple) gives a negative. If the result of multiplying 12 negatives is odd, the largest number of negative integers will be the largest odd number (i.e.10)
so the correct answer is ten!! 


Term
MULTIPLE CHOICE:
If a positive integer n, divided by 10 has a remainder 4, which of the following must be true? 

Definition
I n is odd II n + 2 cannot be a prime number III (n + 4) divided by 14 has remainder 4
A. none B. I only C. I and II only D. II and III only E. I, II and III
Correct Answer: A
Explanation:
You can find the integers which when divided by 10 have a remainder 4 by adding 4 to all multiples of 10. So we have n = 14 , 24, 34, 44 etc. From this series we can see that n does not have to be odd. Also n + 2 can be a prime because, for example, 24 + 2 = 26 And (n + 4) / 14 has a remainder 4 in some cases but not all. Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases. 


Term
Multiple Choice:
A solid rectangle of side 12 is first painted pink and then cut into smaller cubes of side 4. How many of the smaller cubes have paint on exactly 4 sides? 

Definition
A. 60 B. 48 C. 24 D. 16 E. 12
The correct answer is C:24,
Explanation:
When the larger cube is cut into smaller cubes, the corner cubes will have paint on six sides. The cubes in the middle of the faces will have paint on only two sides, but the cubes cut from the edges will have paint on four sides. In this case, there will be only two cubes two on each edge (excluding the corners), and since there are 24 edges, there will be 24 cubes with paint on four sides. 

