PROBLEMS IN STATISTICS AND GEOMETRY

1. GRE QUANT
STATISTICS AND GEOMETRY
PROBLEMS
mathews.suman@gmail.com

2. mathews.suman@gmail.com
NO. FREQ
1 10
2 20
3 18
5 12
NO FREQ
6 24
7 17
8 10
9 9
X and Y have 60 numbers. Average of X = 2.7, Average of Y = 7.1
Z has 120 numbers, 60 numbers in X and 60 in Y
YX

3. mathews.suman@gmail.com
Compare the 2 quantities
Quantity A
Average of 120 numbers in Z
Quantity B
Median of 120 numbers in Z
Mean =
2.7 60 +7.1(60)
120
= 4.9

4. mathews.suman@gmail.com
To find the median, we calculate the cumulative frequency
NO F C F
1 10 10
2 20 30
3 18 48
5 12 60
6 24 84
7 17 101
8 10 111
9 9 120
120
2
= 60
For 60 in the cumulative frequency,
Value of the no is 5
Median = 5
Quantity B is greater

5. mathews.suman@gmail.com
A certain clock has a minute hand exactly 3 times as long as its hour hand.
Point C is at the tip of the minute hand and point D is at the tip of the hour hand.
What is the ratio of the distance that point C and D travel in 6 hours
a). 3:1. b) 6:1. c) 12:1. d) 24:1. e) 36:1
Let the length of the hour hand = x
Length of the minute hand = 3x

6. mathews.suman@gmail.com
Distance covered by the minute hand C in 1 hour = 2𝜋 3𝑥 = 6𝜋𝑥
Distance covered by the minute hand C in 6 hours = 36𝜋𝑥
Since in 1 hour the minute hand covers the entire circumference
1n 12 hours the hour hand D covers the entire circumference.

7. mathews.suman@gmail.com
Distance covered by the hour hand in 12 hours = 2𝜋𝑥
Distance covered by the hour hand in 1 hour =
2𝜋𝑥
12
=
𝜋𝑥
6
Distance covered by the hour hand D in 6 hours = 𝜋𝑥
Ratio of the distance travelled by C : D =
36𝜋𝑥
𝜋𝑥
= 36: 1
Ans = e

8. mathews.suman@gmail.com
o
A B
Length of AB = 14 cm
O is the centre of the circle
Quantity A
Area of the circle
Quantity B
49 𝜋

9. mathews.suman@gmail.com
If d denotes the diameter of the circle ,d> 14 cm
Radius >7 cm
Area >49𝜋
Quantity A is greater
Diameter is the longest chord

10. mathews.suman@gmail.com
P
Q R
6 4
X
Y
Z
9
Triangles PQR and XYZ are similar
PQ= 6 cm, PR = 4 cm, XY = 9 cm
Find length of XZ

11. mathews.suman@gmail.com
If 2 triangles are similar, their corresponding sides are proportional
𝑃𝑄
𝑋𝑌
=
𝑃𝑅
𝑋𝑍
6
9
=
4
𝑋𝑍
XZ = 6 cm
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