Math Practice Problems Review

Question: If 2% of a number is 8, what is that number?
- Options:
- A. $\frac{7}{9}$
- B. $\frac{2}{3}$
- C. $\frac{8}{11}$
- D. $\frac{9}{12}$
- E. $\frac{7}{10}$
- Explanation: To find the original number, use the equation:
  $0.02 \times x = 8$
  Solving for x gives:
  $x = \frac{8}{0.02} = 400$
- Therefore, the correct answer is not listed in the options.

Question: Find the smallest whole number larger than the sum of 22 + 3 + 41.
- Calculation:
  $22 + 3 + 41 = 66$
- Options:
- A. 0.16
- B. 4
- C. 16
- D. 400
- E. 800
- Conclusion: The answer is 67, not among the options listed.

Question: When I open my math book, two pages face me, and the sum of their two page numbers is 317. What is the number of the very next page?
- Explanation: Let the two pages be $p$ and $p + 1$ :
- $p + (p + 1) = 317$
- This implies $2p + 1 = 317$
- Simplifying gives: $2p = 316$ , hence $p = 158$ .
- Next page number: 159.
Options:
- A. 9
- B. 10
- C. 11
- D. 12
- E. 13
- Correct answer: The next page (160) is not an option.

Question: In what range does the value of the following expression occur? $\sqrt{62} + 72$
Options:
- A. 158
- B. 159
- C. 160
- D. 161
- E. 162
Calculation:
- Approximating:
- $\sqrt{62} \approx 7.87 \Rightarrow 7.87 + 72 = 79.87$ .
- The value does not seem to correlate with the provided options.

Question: A factory runs nonstop for three 14-hour shifts, starting with the first shift at 9:00 AM. What time does the third shift end?
Calculation:
- First shift: 9:00 AM to 11:00 PM (14 hours)
- Second shift: 11:00 PM to 1:00 PM (next day)
- Third shift: 1:00 PM to 3:00 AM (next day)
Options:
- A. 12:00 PM
- B. 1:00 AM
- C. 2:00 AM
- D. 3:00 AM
- E. 4:00 AM
Correct answer: D. 3:00 AM.

Question: Maria's Grocery Store buys grapefruits at a cost of 5 for a dollar and sells them at a price of 5 for three dollars. How many must they sell to make a profit of ten dollars?
Calculation:
- Cost for 5 grapefruits: 1 dollar
- Revenue from 5 grapefruits: 3 dollars
- Profit per 5 grapefruits: 3 - 1 = 2 dollars
- To find how many sets of 5 grapefruits are needed to reach a $10 profit:
- $\frac{10}{2} = 5$
- Hence, they must sell $5 \times 5 = 25$ grapefruits in total to achieve a profit of $10.
Options:
- A. <6
- D. 8 to 9

Question: Solve the following: $12 - (-2)^2 - (-2)^3$
Calculation:
- Simplifying:
- $(-2)^2 = 4$
- $(-2)^3 = -8$
- Thus:
- $12 - 4 - (-8) = 12 - 4 + 8 = 16$
Options:
- A. 0
- B. 2
- C. 4
- D. 6
- E. 8
Correct answer: Not indicated in a way that matches any options.

Question: If A # B means the same thing as $2A - B$ , then what does 1 # ((2 # 3) # 4) equal?
Calculation Sequence:
- First, calculate:
  - 2 # 3 = 2(2) - 3 = 4 - 3 = 1
- Then:
  - 1 # 4 = 2(1) - 4 = 2 - 4 = -2
Options:
- A. 15
- B. 17
- C. 19
- D. 20
- E. 25

Question: In hockey standings, a win counts for 2 points, a tie for 1 point, and a loss for 0 points. The Devils won 5, lost 4, and tied 1 game in their first 10 games. If they continue at that rate, how many points will they have after 80 games?
Calculation:
- Points from 5 wins: $5 \times 2 = 10$
- Points from 1 tie: $1 \times 1 = 1$
- Total points from 10 games: $10 + 1 = 11$
- They will repeat this pattern in 80 games, hence:
  $\frac{80}{10} \times 11 = 8 \times 11 = 88$
Options:
- A. 4
- B. 2
- C. 0
- D. -2
- E. -4
Correct answer: D. 88.