TS Police SI Mains 2018 Arithmetic and Reasoning

Instructions

To answer the following questions consider the following information.
Given that
U = {1, 2, 3, ......., 500}
A = the set of all multiples of 6 in U,
B = the set of all multiples of 15 in U and
C = the set of all multiples of 10 in U.
Let $$\mid S \mid$$, denotes the number of elements in a set S. Then

Question 140

$$\mid A \cup B \mid = $$

Solution

n(A U B) = n(A) + n(B) - n(overlap of both A and B)

n(A) = 83 (as 1 to 500 contains 6*1 = 6 to 6*83 = 498)
n(B) = 33 (as 1 to 500 contains 15*1 = 15 to 15*33 = 495)

n(overlap of A and B) = Multiples of LCM of 6 and 15 i.e. 30 from 1 to 500
n(overlap of A and B) = 16 (30*1 = 30 to 30*16 = 480)

Hence, n(A U B) = 83+33-16 = 100


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