IGDTUW 2025 — Mathematics PYQ

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Question

IGDTUW 2025 — Mathematics PYQ

IGDTUW | Mathematics | 2025

If the universal set:

$S = \{x \mid -1 \le x \le 150\}$

$A = \{\text{multiples of } 6\}$

$B = \{\text{multiples of } 10\}$

Then how many elements are there in $(A \cup B) - (A \cap B)$ ?

Choose the correct answer:

Explanation

Solution

To solve this, we find the number of elements ( $n$ ) for each set within the range $1$ to $150$ (since multiples are positive integers):

Set A (Multiples of 6): $n(A) = \lfloor 150 / 6 \rfloor = 25$
Set B (Multiples of 10): $n(B) = \lfloor 150 / 10 \rfloor = 15$
Set $A \cap B$ (Multiples of both 6 and 10, i.e., LCM = 30): $n(A \cap B) = \lfloor 150 / 30 \rfloor = 5$
Symmetric Difference $(A \cup B) - (A \cap B)$ :

The formula is $n(A) + n(B) - 2 \times n(A \cap B)$ .

Calculation: $25 + 15 - 2(5) = 40 - 10 = 30$ .

The correct answer is (a) 30.