MathDB

6

Part of 2014 AMC 12/AHSME

Problems(2)

Difference between Number and its Reverse

Source: 2014 AMC 12A #6

2/5/2014
The difference between a two-digit number and the number obtained by reversing its digits is 55 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?
<spanclass=′latex−bold′>(A)</span>44<spanclass=′latex−bold′>(B)</span>55<spanclass=′latex−bold′>(C)</span>77<spanclass=′latex−bold′>(D)</span>99<spanclass=′latex−bold′>(E)</span>110<span class='latex-bold'>(A) </span>44\qquad <span class='latex-bold'>(B) </span>55\qquad <span class='latex-bold'>(C) </span>77\qquad <span class='latex-bold'>(D) </span>99\qquad <span class='latex-bold'>(E) </span>110
AMC
Drinking Lemonade

Source: 2014 AMC 12B #6

2/20/2014
Ed and Ann both have lemonade with their lunch. Ed orders the regular size. Ann gets the large lemonade, which is 50%50\% more than the regular. After both consume 34\tfrac{3}{4} of their drinks, Ann gives Ed a third of what she has left, and 22 additional ounces. When they finish their lemonades they realize that they both drank the same amount. How many ounces of lemonade did they drink together?
<spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 36<spanclass=′latex−bold′>(D)</span> 40<spanclass=′latex−bold′>(E)</span> 50{ <span class='latex-bold'>(A)</span>\ 30\qquad<span class='latex-bold'>(B)</span>\ 32\qquad<span class='latex-bold'>(C)</span>\ 36\qquad<span class='latex-bold'>(D)</span>}\ 40\qquad<span class='latex-bold'>(E)</span>\ 50
AMC