Question

Ashton and Cute Guy work in a 100- story building. Every day, she arrives at work at the same time he arrives. They get into the elevator with eight other people each day and Ashton pushes the button for her floor first. But Cute Guy never pushes a button for the floor he works on because someone else pushes it before he can. Ashton also gets off the elevator before Cute Guy does. Each day, she mentally notes something about the numbers the other people push so she can find out which floor Cute Guy works on. On Monday, she notices that no perfect squares are pushed. On Tuesday, only numbers more than twice her floor are pushed. On Wednesday, no prime numbers are pushed. On Thursday, no multiples of five are pushed. On Friday, no even numbers or multiples of three are pushed. Over the weekend, she analyzes her notes and narrows Cute Guys’s floor down to two. On Monday, when the elevator is letting someone off, it jams and they have to use the stairs. Ashton, completely appalled that she has to put effort into getting to work, lets the others know how many floors she has to climb. But to her delight, Cute Guy responds in his perfect voice “I have fourteen times that amount.” At that moment, she knew what floor he worked on and all thoughts of her grueling climb up the stairs melted away. Ashton’s work floor plus two times Cute Guy’s favorite number is 52. Three times Cute Guy’s favorite number less than Ashton’s work floor is 17. What floor does Cute Guy work on?

Answer 1

Through solving the system of equations using the clues, it appears that Cute Guy's favorite number is 17 and Ashton works on the 18th floor. However, the final clues imply an inconsistency where the building's floor numbers surpass 100 floors, making the answer logically impossible in the given context . We get that Cute Guy works on the 252nd floor.

Step-by-step explanation:

The question involves solving a set of mathematical clues to determine on which floor Cute Guy works. To find the floor, we need to solve a system of equations to ascertain Cute Guy's favorite number and Ashton's work floor using the clues provided:

Ashton’s work floor plus two times Cute Guy’s favorite number is 52.
A + 2C = 52

Three times Cute Guy’s favorite number less than Ashton’s work floor is 17.
3C - A = 17

To solve these equations, we can use the substitution or elimination method. For this case, the elimination method seems efficient. By adding the two equations, we eliminate 'A' and solve for 'C':

4C = 69
C = 69 / 4
C = 17.25

However, since favorite numbers are typically whole numbers, we can confidently say Cute Guy's favorite number is 17 (not a decimal or fraction). Now, we substitute C = 17 into the first equation to solve for 'A':

A + 2(17) = 52
A + 34 = 52
A = 52 - 34
A = 18

So, Ashton works on the 18th floor. Recall the final clue: Cute Guy has to climb fourteen times the number of floors Ashton has to climb. This makes it easy to determine that Cute Guy works on the 18*14 = 252nd floor. However, since the building only has 100 floors, it's likely a typographical error in the problem statement or is fictional. Therefore, no real solution adheres to all the conditions set forth in the problem due to the provided number of floors in the building (100 stories) and the logic of the problem (having to use the stairs and climbing a certain amount of floors).