Rebecca has a collection of basketball cards. When she puts them in piles of two, she has one card left over. When she puts them in piles of three or four, there is also one card left over, but when she puts them in piles of five there are no cards left over. If Rebecca has fewer than 100 basketball cards, what are the possible numbers of cards she could have?

Rebecca has a collection of basketball cards. When she puts them in piles of two, she has one card left over. When she puts them in piles of three or four, there is also one card left over, but when she puts them in piles of five there are no cards left over. If Rebecca has fewer than 100 basketball cards, what are the possible numbers of cards she could have?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

3. Rebecca has a collection of basketball cards. When she puts them in piles of two, she has
one card left over. When she puts them in piles of three or four, there is also one card
left over, but when she puts them in piles of five there are no cards left over.
If Rebecca has fewer than 100 basketball cards, what are the possible numbers of cards
she could have?

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