Size of a partial deck from three remainders

Some cards have been taken out of a standard $52$-card deck. The number left has remainder $1$ when divided by $3$, remainder $3$ when divided by $5$, and remainder $3$ when divided by $4$. How many cards remain?

$43$. The last two conditions mean the count is $3$ more than a multiple of $20$: $3,23,43$ (below $52$). Only $43$ leaves remainder $1$ on division by $3$.