Odd and even numbers Transitional Reasoning Download PDF

Questions

1. 1.

   A digital platform begins the week with an odd number of registered members. During the week, the platform's membership triples, an even number of additional members join, and finally, exactly one member closes their account. Which statement correctly describes whether the final number of registered members is odd or even?

   • A) The final number is always even, because tripling an odd number produces an odd result, adding an even number keeps it odd, and subtracting one makes it even.
   • B) The final number is always odd, because tripling an odd number produces an even result, adding an even number keeps it even, and subtracting one makes it odd.
   • C) The final number is always odd, because an odd starting number combined with an even number of new members will always result in an odd total regardless of subtraction.
   • D) The final number can be either odd or even, because tripling can produce an odd or even number depending on whether the starting number is prime or composite.
2. 2.

   A community library runs a summer reading challenge where participants record the page counts of four consecutive chapters in a novella. Each chapter has exactly one more page than the preceding one, meaning the four chapter lengths are consecutive whole numbers. Which statement correctly describes the sum of the page counts for any four consecutive chapters?

   • A) The sum will always be odd because adding four whole numbers preserves the parity of the starting chapter.
   • B) The sum will always be even because any four consecutive whole numbers contain exactly two odd numbers and two even numbers, whose sum is always even.
   • C) The sum will be even only if the first chapter has an even number of pages; otherwise, it will be odd.
   • D) The sum will be odd only if the first chapter has an odd number of pages; otherwise, it will be even.
3. 3.

   In a strategy board game, Maya collects three tokens displaying odd numbers and two tokens displaying even numbers. She calculates her round score by multiplying the values on the three odd tokens together and then adding the values on the two even tokens. Which statement correctly describes Maya's total round score?

   • A) The round score must be even because adding two even numbers to any product always makes the total even.
   • B) The round score must be even because multiplying three numbers always produces an even result.
   • C) The round score must be odd because the product of three odd numbers is even, which becomes odd after adding two even numbers.
   • D) The round score must be odd because multiplying three odd numbers produces an odd result, and adding an even sum results in an odd number.
4. 4.

   A robotics club programs a rover to move along a straight testing track. The rover advances 3 meters for each yellow marker it detects and 6 meters for each green marker it detects. During a test, the rover detects an odd number of yellow markers and an even number of green markers. Which statement must be true about the total distance, in meters, traveled by the rover?

   • A) The total distance is always even because 6 meters is an even quantity.
   • B) The total distance can be odd or even depending on how many green markers are detected.
   • C) The total distance is always odd, so it cannot be divided into an exact whole number of 2-meter steps.
   • D) The total distance is always even, so it can always be divided into an exact whole number of 2-meter steps.
5. 5.

   Liam is organizing colored markers for an art project into pairs of 2. He fills 3 red containers with 14 markers each and 2 blue containers with 9 markers each, and he also has 5 loose markers on his desk. If Liam combines all of these markers together, which statement correctly describes the total number of markers and whether they can all be completely paired up?

   • A) The total is 60 markers, which is an even number, so all markers can be grouped into pairs with none left over.
   • B) The total is 65 markers, which is an even number, so all markers can be grouped into pairs with none left over.
   • C) The total is 65 markers, which is an odd number, so exactly 1 marker will be left over without a pair.
   • D) The total is 69 markers, which is an odd number, so exactly 1 marker will be left over without a pair.