benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Betty has between 40 and 50 pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. Ho…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Betty has between 4040 and 5050 pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. However, if Betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. How many pennies did Betty originally have? Note: An a×ba \times b rectangle is considered the same as a b×ab \times a rectangle.
Plain-text mathematical notation (without MathML)
Betty has between 40 and 50 pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. However, if Betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. How many pennies did Betty originally have?

Note: An a×b rectangle is considered the same as a b×a rectangle.
Original LaTeX notation
Betty has between $40$ and $50$ pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. However, if Betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. How many pennies did Betty originally have?

Note: An $a \times b$ rectangle is considered the same as a $b \times a$ rectangle.

level

Level 3

type

Prealgebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
da433141-969c-52a8-908f-29d3bfc20aff
task_key
prealgebra--test--da433141-969c-52a8-908f-29d3bfc20aff
task_revision_id
1
config / split
prealgebra / test

Official source

initial import