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16 Dec 2021, 02:30
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B
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Difficulty:
25%
(medium)
Question Stats:
70% (01:16) correct
30%
(02:17)
wrong
based on 54
sessions
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How many square tiles, each with a side length of n, are needed to completely cover a rectangular floor with dimensions l and m?
(1) n is a factor of both l and m.
(2) n is one half of l and one third of m.
(1) n is a factor of both l and m.
(2) n is one half of l and one third of m.
16 Dec 2021, 03:28
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Bunuel
Basically asking whats the constant we get when we equate area of a rectangle with a sqaure.
Let l be the length of the rectangle
Let m be the width of the rectangle
Let n be the side of the square
Let z be the no of squares needed
l*m = (z)*n^2
We need to find the value of z.
(1) n is a factor of both l and m.
Can be done in two ways will show both:
1)n is a factor of l means nk = l |where k is some multiple of n
n is a factor of m means nq = m |where q is some multiple of n
So new equation
nk*nq =z*n^2
k*q=z
We don't know the value of z and q. Insufficient.
2)Plug in values
let l be 2 and m be 4 and n be 2
In this case z will be 2
let l be 16 and z be 24 and n be 2
in this case z will be 96
No consistent answer. Insufficient
So, A and D are out.
(2) n is one half of l and one third of m.
n= l/2 So, l = 2n
n=m/3 So, m = 3n
So, 6n^2 = zn^2
z = 6. Sufficient.
B is the answer.
Vatsal7794
GMAT 1: 660 Q44 V36
Posts: 246
16 Dec 2021, 04:30
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To determine the no of tiles,We need to find the value of area and to determine value of area we need to have length of sides
No of tiles = L*M / N^2
For statement A we can have several possible values of L and M
From statemenT B we can have L=2n M= 3n
3n*2n \n^2 so answer is 6
Posted from my mobile device
No of tiles = L*M / N^2
For statement A we can have several possible values of L and M
From statemenT B we can have L=2n M= 3n
3n*2n \n^2 so answer is 6
Posted from my mobile device
