Another one:

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

I got the first one:

A = L * W


L+7.5 * W = A+150

LW + 7.5W = LW +150

7.5W = 150

W= 20


L *(W+5) = a +150

LW + 5L = LW +150

5L = 150

L= 30

A= L*w = 20*30 = 600

Answer is A

Hi,
Q1) Keeping width(w) constant, length(l) increased by 7.5 increases area by 150. So 7.5*w=150 =>w=20
Keeping length(l) constant, width(w) increased by 5 increases area by 150. So l*5=150 =>l=20
So, Area of garden =l*w = 30*20 = 600sq ft

Hence, A

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

Hence, D

Thanks but I don't quite get the 2nd one. Anyway here's another one:




Any quick way to solve this? As it'll take some time to point each side size and do pythagoras

Another one:





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

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

l,w,a means length, width and initial area respectively
w(l+7.5) = a+150
lw=a
this w*7.5=150 ->w=20
similarly l(w+5)=150+a -> l=30
area=30*20=600
IMO A

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

area=25. thus side=5
to find least no. of squares, we should use maximum side which is 3.
one 3*3 square. 3 2*2 squares. 4 1*1 squares
total=8
IMO E

Man you asked so many questions in 1 post ....ill post the answer, do tell for which of them u need explanations.

1)A-600
2)D-8
3)C-3.6 .... mark the co-ordinates and use distance formula (2,6,) (5,-1) (-7,-6)
4)E-1/4 .... ratio of area = ratio of sides*ratio of sides ( ques has an error it should show that both verticals are perpendiculars)

MBA.Aspirant wrote:


Any quick way to solve this? As it'll take some time to point each side size and do pythagoras

if we move the triangle ABC up by 0.1 in vertical direction,
A will be (-0.7,-0.5); B(0.5,0); C(.2,.7)
Also it looks like Right angled triangle to me.
AB^2 = 1.2^2 + 0.5^2 -> AB=1.3
BC^2 = .3^2 + .7^2 ->BC=root(.58)=.75
AC^2 = .9^2 + 1.2^2 = 2.25 -> AC=1.5
Thus perimeter = 2.8+.75 = 3.55 = 3.6
IMO C

MBA.Aspirant wrote:Another one:





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

let shorter triangle be BDE
thus BD/BC = DE/AC ->DE/AC=1/2
area BDE/Area ABC = (1/2)(BD)(DE) / (1/2)(AC)(BC) = 1/4
IMO D

cans wrote:

MBA.Aspirant wrote:Another one:





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

let shorter triangle be BDE
thus BD/BC = DE/AC ->DE/AC=1/2
area BDE/Area ABC = (1/2)(BD)(DE) / (1/2)(AC)(BC) = 1/4
IMO D

That's a good way to look at it. I calculated it using the areas.

Small triangle base = 30/root3 = 10 root3

Area = 1/2 * 10 root3 * 30 = 150 root 3

Big triangle base = 20 root 3

Area = 1/2 * 20 root 3 * 60= 600 root 3

Ratio of areas = 150 root3/ 600 root 3 = 1/4

@cans: i think the ques should mentioned that both verticals are perpendiculars, unless we cannot unless property of SIMILAR TRIANGLES.

vikram4689 wrote:@cans: i think the ques should mentioned that both verticals are perpendiculars, unless we cannot unless property of SIMILAR TRIANGLES.

Yeah either perpendiculars or that both vertical lines are parallel
But this is problem solving question and we can't solve any other way. Thus I assumed that.

MBA.Aspirant wrote:Another one:





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

These are similar triangles so ratio of sides is the same and the ratio of any two sides here = 1/2

area = (1/2 * 30 * DE)/(1/2 * 60 * AC) = 1/4 since DE/AC = 1/2

IMO answer is [spoiler]1/4[/spoiler]