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MATH / Suppose that begin{array}{@{}c@{;}c@{}c@{}c} && &P_b & times & & P_b cline{2-4} & & Q & P_b, end{array} where P, Q, and b represent three distinct digits 1-9. If Q=(P)/(2), and …

Problem

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problem

Suppose that $$\begin{array}{@{}c@{\;}c@{}c@{}c} && &P_b \\ & \times & & P_b \\ \cline{2-4} & & Q & P_b, \\ \end{array} $$where PP, QQ, and bb represent three distinct digits 1-9. If Q=P2Q=\frac{P}{2}, and PP is two less than bb, what is the value of the digit PP?
Plain-text mathematical notation (without MathML)
Suppose that $$\begin{array}{@{}c@{\;}c@{}c@{}c} && &P_b \\ & \times & & P_b \\ \cline{2-4} & & Q & P_b, \\ \end{array} $$where P, Q, and b represent three distinct digits 1-9. If Q=(P)/(2), and P is two less than b, what is the value of the digit P?
Original LaTeX notation
Suppose that $$\begin{array}{@{}c@{\;}c@{}c@{}c} && &P_b \\ & \times & & P_b \\ \cline{2-4} & & Q & P_b, \\ \end{array} $$where $P$, $Q$, and $b$ represent three distinct digits 1-9. If $Q=\frac{P}{2}$, and $P$ is two less than $b$, what is the value of the digit $P$?

level

Level 4

type

Number Theory

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Source and history

task_id
e06afe86-7745-575e-8034-7517b57ee93c
task_key
number~5ftheory--test--e06afe86-7745-575e-8034-7517b57ee93c
task_revision_id
1
config / split
number_theory / test

Official source

initial import