MathDB

Problem 1

Part of 2019 LIMIT Category A

Problems(2)

ratio of liquids in can

Source: LIMIT 2019 CAS1 P1

4/28/2021
A can contains a mixture of two liquids A and B in the ratio 7:57:5. When 99 litres of the mixture are drawn and replaced by the same amount of liquid BB, the ratio of AA and BB becomes 7:97:9. How many litres of liquid A was contained in the can initially? <spanclass=′latex−bold′>(A)</span> 18<span class='latex-bold'>(A)</span>~18 <spanclass=′latex−bold′>(B)</span> 19<span class='latex-bold'>(B)</span>~19 <spanclass=′latex−bold′>(C)</span> 20<span class='latex-bold'>(C)</span>~20 <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
ratioalgebra
polynomial interpolation

Source: LIMIT 2019 CAS2 P1

4/28/2021
Let p(x)p(x) be a polynomial of degree 44 with leading coefficient 11. Suppose p(1)=1p(1)=1, p(2)=2p(2)=2, p(3)=3p(3)=3 and p(4)=4p(4)=4. Then p(5)=p(5)=? <spanclass=′latex−bold′>(A)</span> 5<span class='latex-bold'>(A)</span>~5 <spanclass=′latex−bold′>(B)</span> 256<span class='latex-bold'>(B)</span>~\frac{25}6 <spanclass=′latex−bold′>(C)</span> 29<span class='latex-bold'>(C)</span>~29 <spanclass=′latex−bold′>(D)</span> 35<span class='latex-bold'>(D)</span>~35
algebrapolynomial