MathDB

5

Part of 2017 AMC 10

Problems(2)

Sum Products!

Source: 2017 AMC 10A #5, 2017 AMC 12A #2

2/8/2017
The sum of two nonzero real numbers is 44 times their product. What is the sum of the reciprocals of the two numbers?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 12<span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 8\qquad<span class='latex-bold'>(E)</span>\ 12
AMCAMC 10AMC 10 AAMC 12 A2017 AMC 10A2017 AMC 12AAMC 12
Camilla and blueberry

Source: AMC10B 2017 #5

2/16/2017
Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 1010 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?
<spanclass=′latex−bold′>(A)</span>10<spanclass=′latex−bold′>(B)</span>20<spanclass=′latex−bold′>(C)</span>30<spanclass=′latex−bold′>(D)</span>40<spanclass=′latex−bold′>(E)</span>50<span class='latex-bold'>(A) </span> 10\qquad <span class='latex-bold'>(B) </span> 20\qquad <span class='latex-bold'>(C) </span> 30\qquad <span class='latex-bold'>(D) </span> 40\qquad <span class='latex-bold'>(E) </span> 50
AMCAMC 10AMC 10 B2017 AMC 10B