GRE GEOMETRY AND ARITHMETIC

1. GRE GEOMETRY AND
ARITHMETIC PROBLEMS
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2. A horse is tied outside the corner of a shed of length 12 m and breadth 5 m. If the length of the rope is 13 m,
what is the maximum area in which the horse can move.
12m
5m
8m
1m
13m
𝐴 = 𝜋132
4
+ 𝜋
1
4
+
𝜋(64)
4
= 78.5𝑠𝑞 𝑚
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3. 6
A
B
C
D
E
Triangle ABE is inscribed in a circle of radius 6 cm.
BCDE is a square. Find Area of the polygon ABCDE
O
30
M
6
In ∆𝐴0𝑀, cos 30 =
𝐴𝑀
6
𝐴𝑀 = 6 cos 30
6cos30
sin 30 =
𝑂𝑀
6
0M=6sin30
6sin30
∠ABC=60
∠AOE=120
Δ AOE is isosceles
∠OAM=30
AE= 2(
6√3
2
) = 6√3
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ABE is an equilateral triangle

4. A(∆𝐴𝐸𝐵) =
√3
4
(6√3)2
= 27√3
A(square BCDE)=(6√3)2
= 108
𝐴 𝑝𝑜𝑙𝑦𝑔𝑜𝑛 𝐴𝐵𝐶𝐷𝐸 = 27 3 + 108 𝑠𝑞 𝑢𝑛𝑖𝑡𝑠
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5. How many diagonals does a regular 20 sided polynomial have
a) 60
b) 120
c)170
d)240
e)400
Number of lines drawn from 20 vertices is 20𝐶2 as exactly one line can be drawn between 2 points.
(ie no of ways of selecting 2 points at a time from 20 points)
Of these lines, 20 are the sides. Hence no. of diagonals = 20𝐶2 − 20=170
20𝐶2 =
20(19)
2(1)
= 190
Answer = 170
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6. Working alone at its constant rate, machine A produces k parts in 10 minutes, working alone at its constant
rate machine B produces k parts in 15 minutes. How many minutes does it take machines A and B working
simultaneously at their respective constant rates to produce k parts.
Machine A takes 10 min→ 𝑘 𝑝𝑎𝑟𝑡𝑠
1 𝑚𝑖𝑛 →
𝑘
10
𝑝𝑎𝑟𝑡𝑠
Machine B takes 15 min→ 𝑘 𝑝𝑎𝑟𝑡𝑠
1 min→
𝑘
15
𝑝𝑎𝑟𝑡𝑠
Machine A and Machine B ‘s I min work=
𝑘
10
+
𝑘
15
=
𝑘
6
1 min of 𝐴 𝑎𝑛𝑑 𝐵′ 𝑠 𝑤𝑜𝑟𝑘 →
𝑘
6
𝑝𝑎𝑟𝑡𝑠
𝑥 𝑚𝑖𝑛 → 𝑘 𝑝𝑎𝑟𝑡𝑠
𝑘
6
𝑥 = 𝑘
x=6 It takes A and B 6 minutes to produce k parts
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