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square marbles required to tile a floor

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square marbles required to tile a floor

by sanju09 » Wed Jan 13, 2010 5:03 am
What is the minimum number of identical square marbles required to tile a floor of length 5 meter 78 centimeter and width 3 meter 74 centimeter, given that 1 meter length is same as 100 centimeter length?
(A) 176
(B) 187
(C) 216
(D) 748
(E) 54043
Last edited by sanju09 on Thu Jan 14, 2010 12:32 am, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Jan 13, 2010 12:08 pm
sanju09 wrote:What is the minimum number of square marbles required to tile a floor of length 5 meter 78 centimeter and width 3 meter 74 centimeter, given that 1 meter length is same as 100 centimeter length?
(A) 176
(B) 187
(C) 216
(D) 748
(E) 54043
Since there is no mention that the square tiles all must be the same size, the answer is 8

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If the tiles must all be the same size, we are looking for the largest squares to fit in the 578x374 area (without going over the edges since I'm assuming we can't cut these tiles).
So, we are looking for the GCD of 578 and 374

578 = 2x17x17
374 = 2x11x17
The GCD is 2x17 (34)
So, we can use square tiles that have dimensions 34x34

Since the total area is 578x374 and the area of each tile is 34x34, the total # of tiles required will be (578x374)/(34x34)
This equals (2x17x17x2x11x17)/(2x17x2x17) = 11x17 = 187 (B)
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by sanju09 » Thu Jan 14, 2010 12:49 am
Thanks Brent for identifying the ambiguity; edited.
The mind is everything. What you think you become. -Lord Buddha



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