The four-story Willowwood Hotel and Spa has 10 rooms on its

Question

The four-story Willowwood Hotel and Spa has 10 rooms on its top floor. The second and third floors each have 25% more rooms than the bottom floor. Which of the following could not be the total number of rooms in the hotel?

A. 304
B. 350
C. 444
D. 570
E. 612

A. 304
B. 350
C. 444
D. 570
E. 612

paragw · Answer

Here's my solution for this question:

onlyPlanA · Answer

Let x be the number of rooms on the ground floor.
Then number of rooms on both second and third floors = 1.25x

Total rooms in the hotel = x + 1.25x + 1.25x + 10 = 3.5x + 10

Now compare this equation with all the options. An easy way to do this is to subtract 10 from all options and multiply by 2/7.

A) 304
x => (304-10) = 294 * 2/7 = 84
B) 350
x => (350-10) = 340 * 2/7 = 97.something...
No need to check other options.
 B is the answer.

kevincan · Answer

If the bottom floor has x rooms, each of the two floors above it has 5x/4 rooms, and the entire hotel has 7x/2 + 10 rooms

5x/4 is an integer if and only if x is a multiple of 4, i.e. x=4k for some integer . Thus the hotel has 14k +10 rooms. We should look for an answer choice that is not 10 more than a multiple of 14.

304 = 294 + 10 ; 294 = 280 + 14 and is thus a multiple of 14. The hotel could have 304 rooms

350 is multiple of 7 and of 2 and thus is multiple of 14. Thus 350 is not 10 more than a multiple of 14 and so cannot be the number of rooms in the hotel . Success !

444 = 420 +14 + 10

570 = 420 + 140 + 10

612= 570 + 42

Kinshook · Answer

The four-story Willowwood Hotel and Spa has 10 rooms on its top floor. The second and third floors each have 25% more rooms than the bottom floor.

Which of the following could not be the total number of rooms in the hotel?

Let the number of rooms on bottom floor be x.

The total number of rooms in the hotel = y = x + 1.25x + 1.25x + 10 = 3.5x + 10

A. 304 = 3.5x + 10; x = 294/3.5 = 84; feasible
B. 350 = 3.5x + 10; x = 340/3.5=97.143; Not feasible since x is an integer
C. 444 = 3.5x + 10; x = 434/3.5 =124; feasible 
D. 570 = 3.5x + 10; x = 560/3.5=160; feasible 
E. 612 = 3.5x + 10; x = 602/3.5 =172; feasible

IMO B

pappal · Answer

no. of rooms in sequence from bottom= b,1.25b,1.25b,10 where b-rooms on bottom floor
i.e. total no. of rooms=3.5b+10
 in given choices if 10 is subtracted and then multiplied by 10 the resulting no. should be divisible by 35. one that doesn't follow the trend is the correct answer.
lets check 2940,3400,4340,5600,6020.
so B (not divisible by 35)

The four-story Willowwood Hotel and Spa has 10 rooms on its

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