MathDB

15

Part of 2015 AMC 10

Problems(2)

Numerator and Denominator Increased by One

Source: 2015 AMC 10A #15

2/4/2015
Consider the set of all fractions xy,\tfrac{x}{y}, where xx and yy are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 11, the value of the fraction is increased by 10%10\%?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>infinitely many <span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>\text{infinitely many}
SFFTAMCAIMEnumber theoryrelatively prime
Animal Town

Source: 2015 amc 10b #15

2/26/2015
The town of Hamlet has 33 people for each horse, 44 sheep for each cow, and 33 ducks for each person. Which of the following could not possibly be the total number of people, horses, sheep, cows, and ducks in Hamlet? <spanclass=′latex−bold′>(A)</span>41<spanclass=′latex−bold′>(B)</span>47<spanclass=′latex−bold′>(C)</span>59<spanclass=′latex−bold′>(D)</span>61<spanclass=′latex−bold′>(E)</span>66<span class='latex-bold'>(A) </span> 41 \qquad<span class='latex-bold'>(B) </span> 47 \qquad<span class='latex-bold'>(C) </span> 59 \qquad<span class='latex-bold'>(D) </span> 61 \qquad<span class='latex-bold'>(E) </span> 66
AMC