LazyMaths.com

Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

A rectangular bin 4 feet long, 3 feet wide and 2 feet high is solidly packed with bricks of dimensions 8 inches, 4 inches and 2 inches. Find the maximum number of bricks that can go in the bin.

1. 54
2. 320
3. 648
4. 848
5. cannot be determined

The Usual Method

The maximum number of bricks that can go in the bin =

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

Since the size of bins is given in feet and that of the bricks is given in inches, we convert feet to inches by multiplying by 12. Thus the answer should be a multiple of 12. Only option ‘3’ is a multiple of 12.

(Note: to find the multiple of 12, find the multiple of 3 as well as 4).

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.

Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

A certain pole casts a shadow 24 feet long. At the same time another 3 feet high casts a shadow 4 feet long. How high is the first pole given that the heights and shadows are in proportion?

18 feet

19 feet

20 feet

21 feet

22 feet

The Usual Method

Let the height of the pole whose shadow is 24 feet long be ‘x’ feet high.

Since both the length of the poles and its shadow are in proportion, than:

18 feet

(Ans: 1)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

Since height of pole and its shadow are in proportion, we notice that for a pole of 3 feet height, the shadow is 4 feet long. Thus by reducing ¼th (25%) of the length of the shadow, we can get the length of the pole. Thus by doing a 25% reduction on the length of 24 feet long shadow, we can get the height of the pole that casts this shadow.

25% reduction on 24 feet is 24 – 6 = 18 feet.

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.

Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

The equal sides of an isosceles triangle are even integers only. What is the area of the triangle if the perimeter is 7 units?

1. 7 sq. units
2. 3 sq. units
3. 8 sq. units
4. sq. units
5. sq. units

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

Find the areas of the shaded region in the equilateral triangle.

1. sq. units
2. sq. units
3. sq. units
4. sq. units
5. sq.units

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

A large cube is formed from the material obtained by melting three smaller cubes of side 3, 4 and 5 cms. What is the ratio of the total surface areas of the smaller cubes and the large cube?

1. 4 : 3
2. 3 : 2
3. 25 : 27
4. 27 : 20
5. 32 : 15

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

The area of the four walls of a room is 1080 sq.ft. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5. What is the area of the roof?

1. 240 sq.ft.
2. 450 sq.ft.
3. 540 sq.ft.
4. 720 sq.ft.
5. Cannot be determined

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

A circular lawn of 98 meters is surrounded by a path of 14 meters wide. What is the area of the path in meters²?

1. 9420
2. 9184
3. 9240
4. 9835
5. 9583

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

What is the length of the diagonal in the parallelepiped with dimensions 11, 8 and 6 units of length.

1. 13.5 units
2. 14.8 units
3. 10.3 units
4. 19.5 units
5. 25.3 units

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

The figure ABCD is a parallelogram. Find the perimeter of ABCD.
AB =
BC =
DC =
AD =

1. 22
2. 48
3. 53
4. 59
5. 32

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Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

Find the equation of a line with slope –4 and passing through the point (4, 5).

1. x + y = 9
2. x + 4y = 11
3. 4x + y = 21
4. 3x + 2y = 10
5. 5x + y = 30

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