Problem 15 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardcareful-counting
Three frogs live in a pond. Each night only one of the frogs sings a song. After 9 nights the first frog has sung 2 times. The second frog has listened to 5 songs. How many songs did the third frog listen to?
Show answer
Answer: B — 6
Show hints
Hint 1 of 3
There are 9 nights and one song each night, so the three frogs together sang 9 songs.
Still stuck? Show hint 2 →
Hint 2 of 3
On any night, a frog is either singing or listening — so a frog listens on every night it did not sing.
Still stuck? Show hint 3 →
Hint 3 of 3
If the second frog listened to 5 songs, that tells you how many nights it sang instead.
Show solution
Approach: 9 songs in all; a frog listens on every night it does not sing
- There are 9 nights with one song each, so 9 songs were sung in all. Frog 1 sang 2 of them.
- Frog 2 listened to 5 songs, so out of 9 nights it sang on the other 4 nights.
- That leaves Frog 3 singing 9 take away 2 take away 4, which is 3 nights, so it listened on the other 6 nights: 6, option B.
Mark:
· log in to save