problems on pie chart and polygons in the GRE QUANT

1. GRE QUANT:
PIE CHARTS, POLYGONS

2. PHOTOGRAPHIC EQUIPMENT PRODUCTION
SENSITIZED GOODS MOTION PICTURE EQUIPMENT PREPARED PHOTOCHEMICALS
MICROFILM OFFICE COPIES STILL PICTURE EQUIPMENT
47%
12%
5%
7%
4%
25%
IOF 3980 MILLION
In 1971

3. a) Approximately what was the ratio of the value of sensitized goods to the value of still
picture equipment produced
Ratio =
47%
12%
𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 4 ∶ 1
b) If the value of office copies produced in 1971 was 30 % greater than the corresponding
value in 1970, what was the value of the office copies produced in 1970

4. Let the value of the office copies produced in 1970 = x
Value in 1971 =
30
100
× 𝑥 + 𝑥 = 𝑥 +
3𝑥
10
= 1.3𝑥
𝑉𝐴𝐿𝑈𝐸 𝑖𝑛 1971 =
25
100
× 3980 = 995 𝑚𝑖𝑙𝑙𝑖𝑜𝑛
1.3 x = 995
𝑥 = 765 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 = 𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 1970

5. Question 2
How many unique triangles can be inscribed in the vertices of an octagon, if points
A and B, 2 vertices in the octagon cannot make up the same triangle
Number of triangles formed from the vertices of an octagon =8 𝐶3
= 56
To find the number of triangles that contain A and B
Fix A and B , One point remaining can be chosen from the remaining 6 points in 6 ways

6. Number of triangles that contain A and B = 6
Number of triangles that do not contain A and B = 56- 6 =50
Question 3
A rectangular cuboid of volume 3200𝑚𝑚3 ℎ𝑎𝑠 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑏𝑎𝑠𝑒 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 10 𝑚𝑚
and width 8mm. Find the height of the cuboid
Volume = 𝑙 × 𝑤 × ℎ
3200= 10× 8 × ℎ
h = 40 mm

7. Question 4
How many diagonals are there in a regular polygon of 6 sides
A regular polygon of 6 sides has 6 vertices
Number of lines that can be formed using these 6 vertices = 6 𝐶2
= 15
Of these 6 lines, 6 are the edges
Number of diagonals = 15 - 6 = 9
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