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A rectangular floor that is 10 feet wide
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08 Jun 2019, 04:15
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A rectangular floor that is 10 feet wide and 17 feet long is tiled with 170 one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
Re: A rectangular floor that is 10 feet wide
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21 Nov 2024, 08:20
Expert Reply
The number of square tiles visited will be 17 + 9 = 26
The logic is this: From A to C, the ant will cover 17 tiles.
But from A to D, the ant will cover 17 + 2 = 19 tiles. Since there are three rows, every time the ant crosses from one row to another row, it crosses two tiles (shown by the coloured tiles). So for every extra row, it covers one extra tile.
Since we have to cover 10 rows, the number of tiles crossed will be 17 + 9 = 26
Re: A rectangular floor that is 10 feet wide
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23 Nov 2024, 02:38
"The logic is this: From A to C, the ant will cover 17 tiles.
But from A to D, the ant will cover 17 + 2 = 19 tiles. Since there are three rows, every time the ant crosses from one row to another row, it crosses two tiles (shown by the coloured tiles). So for every extra row, it covers one extra tile.
Since we have to cover 10 rows, the number of tiles crossed will be 17 + 9 = 26"
Please how would you know there are 2 additional tiles without actually drawing this all out in the exam
A rectangular floor that is 10 feet wide
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23 Nov 2024, 07:02
Expert Reply
1. For first 1 m along the width, bug will travel 1.7 m along the length or he has to travel through 2 tiles. {Up to 1 m along the length, he will travel through 1 tile and from 1 to 1.7m along the length, he will travel through 2nd tile. Similarly we will find number of tiles he will visit for next 9 cases}
2. For second 1 m along the width, bug will travel to 3.4 m along the length or he has to travel through 3 tiles. 3. For third 1 m along the width, bug will travel to 5.1 m along the length or he has to travel through 3 tiles. 4. For fourth 1 m along the width, bug will travel to 6.8 m along the length or he has to travel through 2 tiles. 5. For fifth 1 m along the width, bug will travel to 8.5 m along the length or he has to travel through 3 tiles. 6. For sixth 1 m along the width, bug will travel to 10.2 m along the length or he has to travel through 3 tiles. 7. For seventh 1 m along the width, bug will travel to 11.9 m along the length or he has to travel through 2 tiles 8. For eighth 1 m along the width, bug will travel to 13.6 m along the length or he has to travel through 3 tiles 9. For ninth 1 m along the width, bug will travel to 15.3 m along the length or he has to travel through 3 tiles 10. For last 1m along the width, bug will travel to 17 m along the length or he has to travel through 2 tiles.
On total number of tiles, bug will visit= 2+3+3+2+3+3+2+3+3+2=26
gmatclubot
A rectangular floor that is 10 feet wide [#permalink]