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02 Dec 2021, 07:39
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D
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Difficulty:
45%
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Question Stats:
67% (02:01) correct
33%
(02:16)
wrong
based on 64
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The seats at the Rio Theater are arranged in rows, with the same number of seats in each row. If there are 600 seats in total in the Theater, how many seats are there in each row?
1) If one seat was added to each row, there would be 624 seats in total in the Theater.
2) If one seat was removed from each row, the number of rows would be equal to the number of seats in one row.
1) If one seat was added to each row, there would be 624 seats in total in the Theater.
2) If one seat was removed from each row, the number of rows would be equal to the number of seats in one row.
18 Dec 2021, 06:05
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This question is from one of my books, my book on GMAT Algebra. I wrote it mainly to illustrate a useful algebraic shortcut, but I'll let others try to solve it before explaining further.
18 Dec 2021, 09:15
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Quote:
The seats at the Rio Theater are arranged in rows, with the same number of seats in each row. If there are 600 seats in total in the Theater, how many seats are there in each row?
1) If one seat was added to each row, there would be 624 seats in total in the Theater.
2) If one seat was removed from each row, the number of rows would be equal to the number of seats in one row.
1) If one seat was added to each row, there would be 624 seats in total in the Theater.
2) If one seat was removed from each row, the number of rows would be equal to the number of seats in one row.
Given that there were originally 600 seats, and that adding 1 seat per row would give 624 total, we can infer that there are (624-600) = 24 rows. (1) is sufficient.
(2) tells us that removing 1 seat per row will give Row x Seat = R^2 = S^2
The closest square root of 600 is 625 (25*25).
24*24 gives 576... which if we add back the 24 removed seats, gives us the 600 original number of seats in the Theatre. (2) is sufficient.
Ans: D - Either statement ALONE is sufficient.
