Set Theory, Calendars, Clocks and Binomial Theorem

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Set Theory: Number of Elements

    Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many elements are present in ?
    1. 202
    2. 243
    3. 228
    4. 186

 

  • Correct Answer
    Choice A. 202

Explanatory Answer

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Detailed Solution

This question involves both Number Systems and Set Theory.

Set P = {4, 8, 12, ….496} 124 elements {all elements from 1 x 4 to 124 x 4}

Set Q = {7, 21, 35, 49,……497} {7 × 1, 7 × 3, 7 × 5, ….. 7 × 71} 36 elements.

Set R = {6, 12, 18, 24, …..498} {6 × 1, 6 × 2, 6 × 3, ….. 6 ×83} 83 elements.

Sets P and R have only even numbers; set Q has only odd numbers. So,

= Null set

= Null set

= Null set

So, If we find , we can plug into the formula and get

= Set of all multiples of 12 less than 500 = {12, 24, 36,…..492 = {12 × 1, 12 × 2 , 12 × 3, …12 ×41} This has 41 elements

= P + Q + R – () – () – () + ()

= 124 + 36 + 83 – 0 – 0 – 41 + 0 = 202

Answer choice (a)

Correct Answer: 202.



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