NIMCET 2011 — Reasoning PYQ

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Question

NIMCET 2011 — Reasoning PYQ

NIMCET | Reasoning | 2011

If from 4 to 55 the numbers which are divisible by 3 and the numbers which contain 3 as one of the digits, are removed, then how many numbers will be left ?

Choose the correct answer:

Explanation

1. Total numbers in the range:

The numbers are from $4$ to $55$ .

\text{Total numbers} = 55 - 4 + 1 = 52

2. Numbers divisible by $3$ ( $Set A$ ):

The multiples of $3$ between $4$ and $55$ are:

$6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54$

\text{Count of } n(A) = 17

3. Numbers containing the digit '3' ( $Set B$ ):

The numbers between $4$ and $55$ that have $3$ as a digit are:

$13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53$

\text{Count of } n(B) = 14

4. Numbers common to both sets ( $A \cap B$ ):

These are numbers divisible by $3$ AND containing the digit $3$ :

$30, 33, 36, 39$

\text{Count of } n(A \cap B) = 4

5. Total unique numbers to be removed ( $A \cup B$ ):

Using the formula: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

n(A \cup B) = 17 + 14 - 4 = 27

6. Numbers left:

\text{Remaining numbers} = \text{Total} - n(A \cup B)

\text{Remaining numbers} = 52 - 27 = 25

Correct Option: (d) $25$