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Number of values of floor perimeter possible
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16 Aug 2020, 04:15
16 Aug 2020, 04:15
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Andrew has 400 tiles of dimension 1 unit x 1 unit each. He wants to build a 4 walled room with the floor completely covered with these tiles. How many distinct values of the floor perimeter are possible?
A) 10
B) 7
C) 8
D) 12
A) 10
B) 7
C) 8
D) 12
Re: Number of values of floor perimeter possible
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16 Aug 2020, 13:38
16 Aug 2020, 13:38
Expert Reply
Sir
Could you provide me the iD of the question considering you have tagged it as GPC question ??
Also one answer is missing
Could you provide me the iD of the question considering you have tagged it as GPC question ??
Also one answer is missing
Re: Number of values of floor perimeter possible
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16 Aug 2020, 15:43
16 Aug 2020, 15:43
1
Longer Way:
Since the floor will use all 400 tiles its area is 400
Therefore length*width=400
Since the tiles are 1*1 units. We want to find all the possible pairs of positive integers that multiple to 400. THis is equivalent to finding all possible different perimeter values.
(1,400)
(2,200)
(4,100)
(5,80)
(8,50)
(10,40)
(16,25)
(20,20)
Total: 8
Final Answer: C
Quick Way:
Prime factorization of 400 is 2^4*5^2
The number of factors of 400 is therefore (4+1)(2+1)= 5*3 =15
15 is odd therefore one factor multiplies with itself to get 400. (20*20)
14/2=7 distinct pairs
7+1=8
(we added one to count the pair 20*20)
Final Answer: C
Since the floor will use all 400 tiles its area is 400
Therefore length*width=400
Since the tiles are 1*1 units. We want to find all the possible pairs of positive integers that multiple to 400. THis is equivalent to finding all possible different perimeter values.
(1,400)
(2,200)
(4,100)
(5,80)
(8,50)
(10,40)
(16,25)
(20,20)
Total: 8
Final Answer: C
Quick Way:
Prime factorization of 400 is 2^4*5^2
The number of factors of 400 is therefore (4+1)(2+1)= 5*3 =15
15 is odd therefore one factor multiplies with itself to get 400. (20*20)
14/2=7 distinct pairs
7+1=8
(we added one to count the pair 20*20)
Final Answer: C
