Geometry

Quote:
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Cans!! could you please explain this in a more elaborate manner...
Why do we need 1 and 2 inches when we can get least number squares using 3 and 1 only. This will give us the required value.

MBA.Aspirant wrote:The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

(A) 600 (B) 525 (C) 375 (D) 300 (E) 225

Area = (l*b) = (l+7.5)*b - 150 ---- (i)
Area = (l*b) = l*(b+5) - 150 ------ (ii)

solving, l = 1.5b

putting in either equation, l = 30, b = 20.
area = 600

option A

MBA.Aspirant wrote:Another one:





I don't get the notations on the sides.. is the ABC side = 60 or 60+30?

let the line parallel to AC be x,
using similar triangle ratio,
x/AC = 30/60

the ratio is thus,
(1/2 * x * 30 / (1/2 * AC * 60) = 1/4

[email protected] wrote:Quote:
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Cans!! could you please explain this in a more elaborate manner...
Why do we need 1 and 2 inches when we can get least number squares using 3 and 1 only. This will give us the required value.

Q2)No. of 3x3 squares that can be cut = 1(from a corner) --> 9 sq.inches
From the remaining part (16sq.inches), 4 (2x2) cannot be cut.
So, no. of 2x2 squares that can be cut = 3(from remaining part)-->3*(2*2)=12 sq.inches
That leaves 4sq units i.e. 4 (1x1) squares
So, total=1+3+4 = 8

You can use maximum 1 3*3 square.
Because when you use that, no more space for extra 3*3 remains.
Now if you use only 3's and 1's;
3*3 covers 9 1*1 squares. Total we have 25 1*1 squares
Thus remaining = 16 1*1 squares
Thus you need to use 16 +1 total = 17
17>8
Thus not correct.