UND MATHEMATICS TRACK MEET Individual Test 4

University of North Dakota Grades 9/10
January 12, 2026
School Team Name
Calculators are NOT allowed. Solutions Student Name

• 1.

  In a survey, 130 students were asked if they liked dogs and if they liked cats. A total of 90 students like dogs. A total of 67 like cats. A total of 13 like neither cats nor dogs. How many of the 130 students like both cats and dogs?

    (2 pts) 1. 40

  Solution: $90+67-x+13=130⟹170-x=130⟹x=40$

• 2.

  A 24-hr digital clock shows a time of 12:34. How many minutes will pass until the clock next shows a time in which all of the digits are consecutive and are in increasing order?

    (3 pts) 2. 671 min

  Solution: The next time is 23:45, the amount of time gone by is 11 hours and 11 minutes. $11(60)=660$ and $660+11=671$ minutes

• 3.

  Your car is currently 3 years old and is worth $10,000. Three years ago, it was worth $13,000. Assume the car’s value depreciates linearly with time. What will be the value of the car in 5 years?

    (3 pts) 3. $5000

  Solution: Two points (0,13000) and (3, 10000). We know the model fits this form $y=mx+b$. We need to find $m$ and $b$, the initial point is given so $b=13000$ and $m=\frac{13000-10000}{0-3}=-1000$. Then to find the value after 8 years, we have $y=-1000(8)+13000=5000$

• 4.

  An urn is filled with coins and beads, all of which are either silver or gold. Ninety percent of the objects in the urn are beads. Sixty percent of the coins in the urn are silver. What percent of the objects in the urn are gold coins?

    (3 pts) 4. $4\%$

  Solution: $0.9+g+s=1$ were $g$ percentage of gold coins and $s$ is silver coins.
  $s=0.1(0.6)=0.06$, then $0.9+g+0.06=1⟹g=0.04$

• 5.

  A number is multiplied by seven and then sixty-two is subtracted from the result to give ninety-nine. What is the original number?

    (3 pts) 5. 23

  Solution: $7x-62=99⟹7x=161⟹x=23$

• 6.

  The triangular prism shown below has a volume of 10. A new prism is formed by doubling the base and height of the original triangle, and tripling the length of the original prism. What is the volume of the new prism?

    (3 pts) 6. 120

  Solution: $\frac{1}{2}bhl=10$ the new prism is

  $$\frac{1}{2}bhl=10⟹\frac{1}{2}(2b)(2h)(3l)=12(\frac{1}{2}bhl)=12(10)=120$$

• 7.

  Real numbers $a$ and $b$ satisfy the equations $3^a={27}^{b+1}$ and ${32}^b=2^{2(a-4)}$. What is $ab$?

    (3 pts) 7. 18

  Solution: Rewrite to have the same base $3^a=3^{3(b+1)}$ and $2^{5b}=2^{2a-8}$. Now, $a=3(b+1)$ and $5b=2a-8$ such that $5b=2(3(b+1))-8⟹5b=6b+6-8⟹b=2$. Next, $a=3(2)+3=9$. Finally, $ab=2(9)=18$