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14 May 2019, 00:13
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Difficulty:
95%
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Question Stats:
27% (02:32) correct
73%
(02:26)
wrong
based on 85
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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?
A. 17
B. 25
C. 26
D. 27
E. 28
A. 17
B. 25
C. 26
D. 27
E. 28
15 May 2019, 13:54
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the equation of the diagonal line is y= 10x/17 As x goes in integer steps from 0 to 17, y only takes integer values at x=0 and x=17.
Draw the diagram and check the equation for points that are confusing. For e.g. when x=5, y= 50/17 (a little less than 3)
Draw the diagram and check the equation for points that are confusing. For e.g. when x=5, y= 50/17 (a little less than 3)
01 Jun 2019, 18:46
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Bug will travel along diagonal, that makes\(tan^{-1}(10/17)\) angle with the length of the floor. In other words, bug will travel 1m along the width for every 1.7m along the length.
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
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
Bunuel
