Reasoning: (x + 1)! = (x + 1) (x+2)* x!
(x + 1)!/x! = (x + 1)(x+2)
Ans: (E)
Question: Which of the following is equal to (x+2)!/x!?
Options:
(A) x-1
(B) 1+(1/x) 
(C) 1
(D) x+1
(E) (x+1) (x+2) 
Rationale: 6a2 = 6 * 3a * 3a = 54a2
The answer: (B)
Question: The edge of a cube is 3a cm. Find its surface?
Options:
(A) 64a2 cm2
(B) 54a2 cm2
(C) 84a2 cm2
(D) 24a2 cm2
(E) 34a2 cm2
Reasoning: 3 hours at a speed of 20 miles per hour gives us Distance = 20*3 = 60 miles
6 hours at a speed of 30 miles per hour gives us Distance = 30*6 = 180 miles
1 more hour at 40 miles per hour gives us Distance = 40*1 = 40 miles
Total Distance = 60+180+40 = 280 miles
Total Time = 3+6+1 = 10 Hours
Average Speed = 280 / 10 = 28 Miles per hour
Ans: (C)
Question: Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?
.
Options:
(A) 25
(B) 27.5
(C) 28
(D) 30
(E) 32
Rationale: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.
The answer: (C)
Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
Options:
(A) 5
(B) 8
(C) 7
(D) 6
(E) 4
Reasoning: Assume the price = 100
Price during sale = 90
Price after sale = 100
Percent increase = 10/90*100 = 11% approx.
Ans: (C)
Question: During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Options:
(A) 9%
(B) 10%
(C) 11%
(D) 15%
(E) 90%
Reasoning: Given: x≥−3x≥−3 and x≤2 x≤2
(x+3)≥0(x+3)≥0 and (x−2)≤0(x−2)≤0
(x+3)≥0(x+3)≥0 and (2−x)≥0(2−x)≥0
Ans: (D)

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Question: The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?
Options:
(A) (3+x) (2−x)  ≤ 0
(B) (3−x) (2+x)  ≥ 0
(C) (x−3) (x+2)  ≤ 0
(D) (x+3) (2−x)  ≥ 0
(E) (3−x) (2−x)  ≥ 0