Negative numbers and the number line Transitional Reasoning Practice

Questions

1. 1.

   A digital monitoring system records the temperatures of different cold-storage rooms as integers on a number line, where negative values represent degrees below freezing. Room P is maintained at $-14^\circ\text{C}$, Room Q is at $-5^\circ\text{C}$, and Room R is at $-2^\circ\text{C}$. Room S is colder than Room Q, warmer than Room P, and located strictly closer to Room P than to Room R on the number line. If the temperature of Room S is an integer multiple of 4, what is the temperature of Room S?

   • A) $-6^\circ\text{C}$
   • B) $-8^\circ\text{C}$
   • C) $-12^\circ\text{C}$
   • D) $-16^\circ\text{C}$
2. 2.

   In an underwater research grid, locations along an east-west axis are represented on a number line where a central dock is at 0 and locations to the west are represented by negative integers. Sensor A is anchored at -30 and Sensor B is anchored at -6. Three relay buoys are placed strictly between Sensor A and Sensor B to divide the segment connecting them into four equal parts. Which integer corresponds to the location of the relay buoy closest to the central dock?

   • A) -12
   • B) -18
   • C) -24
   • D) -6
3. 3.

   On a straight testing track marked in metres, the central calibration point is designated as 0, positions to the east are positive integers, and positions to the west are negative integers. A remote-controlled inspection cart starts at point P at -15 and travels east to point Q, which represents the opposite integer of P. From point Q, the cart then travels west by a distance equal to one-third of the total distance between P and Q to reach its final stop at point R. Which integer represents the cart's final position at point R on the track?

   • A) -5
   • B) 0
   • C) +5
   • D) +10
4. 4.

   A mountain weather station monitors air temperature changes relative to the freezing point of $0^\circ\text{C}$ on a vertical temperature scale. At sunset, the recorded temperature was $-4^\circ\text{C}$, after which it dropped by $5^\circ\text{C}$ by midnight and then rose by $3^\circ\text{C}$ by sunrise. What was the temperature at sunrise, and what is its distance from $0^\circ\text{C}$ on the number line?

   • A) $-12^\circ\text{C}$, with a distance of $12$ units from $0$ on the number line
   • B) $-6^\circ\text{C}$, with a distance of $6$ units from $0$ on the number line
   • C) $-6^\circ\text{C}$, with a distance of $-6$ units from $0$ on the number line
   • D) $-2^\circ\text{C}$, with a distance of $2$ units from $0$ on the number line

Answers and step-by-step solutions appear after you finish the test.